In between big mouthfuls of kulera ba qima, a Kurdish dish of bread and ground beef, Warzer Jaff – stubble, hair gel, traditional baggy Kurdish trousers and cumberbund – is trying to explain why his city is different. “People in Sulaymaniyah are like wild horses,” he says. “Nobody can control them. They live to be against power.”

Jaff, a photographer who moved to New York in 2007 and is back home visiting family, finishes his food, gulps down a plastic cup of water and places his hands on the café’s Formica table. “What I’m trying to say is this: we’re a pain in the ass.”

It is a role that Sulaymaniyah, the cultural heart of Iraqi Kurdistan, perched in the shadow of the Goixa hills in the northeastern corner of Iraq, has been proudly playing since its creation 225 years ago. The city’s first ruler, Ibrahim Pasha Baban, called for artists and professionals to make their homes here. Unlike Erbil and Duhok, both of which started life as villages and only became fully fledged cities in the 20th century (a fact repeated often here with something approaching smug satisfaction), Sulaymaniyah built itself a reputation based on creativity and intellectualism. It is also renowned for opposition to central government, whether in Kurdish Baban, Mesopotamia or, most brutally, Saddam Hussein’s Iraq. Now it is doing it again, a defiant thorn in the side of the Kurdistan Regional Government.

Asos Hardi lowers his head to show the 32 stitches he needed after being pistol whipped six times late one night. “It’s the Kurdish model of democracy,” he says with a grin. Hardi is the founder and editor of one of Kurdistan’s only independent newspapers, Awene. His office looks like it hasn’t had a makeover since the 1970s. The sofas have paisley patterns, the carpets and curtains are stained and the smell of stale cigarette smoke clings to every piece of fabric. A well-thumbed copy of Journalism: Theory and Practice sits on his desk.

Hardi has some of the same problems that are inflicting western newspapers: a falling print circulation as advertising revenue plummets and readers switch to smartphones. As the stitches show, he also has to deal with powerful forces that would prefer independent journalism not to be a part of the new Kurdistan.

Protests erupted in Sulaymaniyah two years ago, inspired by the Arab uprisings in Tunisia and Egypt. In some ways they were a sign of progress for Kurdistan: the protests were against their own government rather than Baghdad. But the way they were dealt with – police violence, widespread arrests, attacks on journalists – were worrying signs.

Twana Osman also has war wounds to show, though his are to property. The director of nrt, Kurdistan’s first independent television station (the rest are all owned by, or affiliated with, political parties), prefers to take the stairs to his second-floor office when he has visitors to show around. The tour takes him past rooms burned down by the police after nrt had the temerity to broadcast footage of the demonstrations. “It was our first day on air,” Osman says. Despite the violence – all staff had been warned of the police’s imminent arrival and made themselves scarce – Osman has no doubt that he chose the right city to be based in. “The atmosphere is more open for media work. We’re different here.”

That difference is emphasised by Pary Tahir, a female news anchor who presents three bulletins a day. Wearing a glamorous blouse and jacket, she has just finished the 21.00 news and rises from her seat to reveal the desk was hiding her jeans. nrt, she claims, is “the Kurdish Al Jazeera”, a lone independent voice in a media landscape where everything else is owned by a political party. Her mother wasn’t happy about her taking this job. “The neighbours would say bad things,” when she returned home late at night. But her onscreen popularity has helped. “All the time girls stop me in the street and say, ‘Mum, can I have my picture with her?’”

The following morning, monocle is sat in a café to witness heads turn as Kotayi, Diana and Parez enter. Kotayi’s hair extensions reach the backs of her thighs, Diana’s trilby is worn at a deliberate angle and Parez’s nails sparkle with fake diamonds. They are confident, stylish and outgoing – until, that is, monocle asks to take their picture. Kotayi, at 23 the oldest of the three, says she needs to ask her brother for permission. A 20-minute phone call ensues. It’s fine, she says: he gives his approval.

The three women live in Kirkuk, some 100km away to the southwest but culturally many million miles from Sulaymaniyah’s relatively liberal outlook. To wear such clothes in Kirkuk would be “impossible”, says Diana. “I wear the hijab there.”

Diana wants to be a doctor, Kotayi a teacher and Parez an engineer, although she also harbours ambitions of becoming a designer. “I’m trying to create my own designs,” she says. “Our cities are developing like crazy but the people are conservative.” On cue, the women are joined by two men, Shamiran and Hunar, both 24, who take over the conversation. Shamiran appears confrontational: broad shouldered, unsmiling, arms crossed and aggressive. And then he speaks: “Sulaymaniyah was the first place a woman drove a car in Iraq – in 1934, she was a pharmacist. It was the first city run by a woman. Sulaymaniyah is different.”

Sulaymaniyah’s differences – its more liberal way of life, the presence of Kurdistan’s first hip-hop act (they’re called Losing Space), its first death metal act (Beneath Eternal Oceans of Sand), its poets, playwrights and crusading journalists – don’t just shape the city but are beginning to mould the country that Kurdistan might become. Iraqi Kurdistan is entering its second decade of autonomy, enjoying a loose freedom from Baghdad that has taken many decades to win. The dream of independence still exists but for many Kurds the reality of autonomy is enough to be getting on with.

The greater dream is Greater Kurdistan, a union of the four Kurdish regions in Iraq, Iran, Syria and Turkey. That ambition remains seemingly unreal, a misty-eyed topic of conversation in Sulaymaniyah tea houses under the gaze of creased and faded Kurdish heroes pinned to the wall. Yet the prospect of it becoming a reality has never been closer. Peace talks in Turkey between the government and Abdullah Ocalan’s pkk have led to a ceasefire; Kurdish rebels in Syria now control much of their own territory. The idea of what Kurdistan could look like, how it could work, is no longer quite so fanciful.

To be able to build the future it is important to remember the past. The physical reminders of Saddam’s legacy in Sulaymaniyah attract a playful curiosity. In the grounds of the old headquarters of the Mukhabarat, Saddam’s secret police, families clamber over the rusting tanks that once fired on Kurdish protestors, grinning and laughing as they pose for pictures straddling guns or lowering themselves through the hatches. Two teenage boys sprint into one of the prison cells, wrap themselves in blankets strewn on the floor and model for a friend’s smartphone camera. This was where Saddam “tried to delete the Kurdish identity,” says Ako Ghareb Maroof, the man who runs the museum now housed in this collection of concrete outhouses and crumbling redbrick buildings where Kurds were tortured.

“We crossed a river of blood of the martyrs,” says the sombrely suited Maroof. “Other generations must not forget how we reached today.” Maroof knows what he’s talking about – few people would be as well suited as he is to run this place. He graduated from Sulaymaniyah’s fine-art institute in 1985 but swapped his paintbrushes for a Kalashnikov, heading into the hills to join the Peshmerga. It was a battle that ostensibly lasted until 1991, when the Kurds won a degree of autonomy, and ultimately came to a complete halt in 2003 when the US invasion of Iraq took place.

Now Kurdistan has peace it has the opportunity to tell its own story. “Other people were writing our history,” says Maroof. “Other people were taking credit for our art. We had to stand up and start again with everything owned by ourselves. We are not fighting our enemies anymore. We are building our society.” That society, he says, is Greater Kurdistan. “We are a country but it’s unfinished.” Indeed, he fears it will not be finished for generations to come. “I hope, but no.”

The Kurdishisation of Kurdistan extends to the spelling of Sulaymaniyah. Half a dozen variations adorn official signposts, posters and government buildings across the city. At the city’s museum, the sign outside calls it Slemani; the brass plaque inside reads Sulaimany. The former is Kurdish, the latter Iraqi. Hashim Hama Abduallaha, the bright-eyed museum director, fiddles with the screws of the inside plaque. “I need to change it,” he sighs. “It’s Baghdad thinking.”

Abduallaha is familiar with Baghdad thinking – and isn’t always against it. He studied there in the 1980s and today has a good relationship with the city’s museum. It hasn’t always been that way. In 1991, the Iraqi army tried to empty the Sulaymaniyah museum and take all the artefacts to Baghdad – they were stopped by the Peshmerga. Even recently, Iraq’s tourism minister called for Sulaymaniyah museum to be closed down.

Abduallaha has two ambitions. Firstly he wants to use the museum to promote Kurdish culture and history to the country’s own people. “We have to remove the filter from our eyes,” he says. Perhaps more importantly, he wants the world to know the importance of Kurdistan.

Sulaymaniyah’s culture, from the 100,000-year-old stones found in the museum to the paintings created by artists such as Salar Majid, will help tell that story. In his first-floor studio, deep inside the city’s bazaar, Majid flicks through old artwork. “We used art to protect ourselves, like fighting,” he says, alighting on heartbreaking abstract paintings inspired by Saddam’s gassing of Halabja in 1988. And now? He smiles a beautiful smile. “No, now I’m in love.” He displays more painting – the colours are stronger, the light is brighter. “I am swimming in beauty. My life is swimming in that magic.”

That sense of optimism is found throughout this city, whether it’s the young women from Kirkuk ecstatic at their one day of sartorial freedom or the old newspaper editor with 32 government-enforced stitches in his head. People from Erbil may joke about Sulaymaniyah but many would privately admit they’d rather live here. Turkish, Syrian and Iranian Kurds don’t have their own country, maybe never will. They don’t even have their own Sulaymaniyah yet. But if they ever have the chance to build their own Kurdish nations, Sulaymaniyah, this city where everyone is “a pain in the ass”, where they “swim in the magic”, will be the city they turn to for inspiration.

The Iraq war was a disaster from start to finish, yet visiting Kurdistan makes one pause. The words “liberation” and “freedom” are not said with irony here. The aftermath of the US-led invasion brought peace, not chaos.

Kurdistan now controls its own destiny – it wouldn’t if Saddam was still in power. Given the sectarian violence that has torn the heart out of much of the rest of the country, peace in one corner does not make the whole endeavour worthwhile. But when the history of the Iraq war is written, Kurdistan’s relatively stable present and bright future cannot be ignored.

There can be a disconnect between those who remained in Kurdistan during Saddam’s years and those, like Kamaran Showqi, who left and returned. Showqi, a grumpy bear of a man, was jailed “two or three times” during the 1980s before fleeing to Stockholm, then Moscow. “Death was near me,” he says. “Leaving was horrible but it was better.” His return, a decade ago, was not smooth. Hopes of creating a film institute in Sulaymaniyah died a slow death. “Politics now is not about honour or humanity,” he says. “They don’t think about culture. If they do, they think about how to use culture to get money. Those who didn’t leave act weird with us who did – they thought we were in paradise. They think I am back to take over. I’m not welcome.”