In the summer of 2003, Ana Lily Amirpour flew from Los Angeles to Iran, the country of her parents. A young American woman in Tehran with an eccentric haircut and a nose piercing, Amirpour was advised to wear the chador, a full-length robe that leaves only the face exposed. She still stood out; she was heckled and spat on by older women. But she liked the way the fabric caught the air: it moved like a cape. She felt, she realised, like a bat.

Twelve years later, Amirpour is having breakfast in a London hotel restaurant, a small, animated figure with a shag of brown-black hair. “I felt like a badass,” she says. “I thought: ‘OK, obviously this is an Iranian vampire.’”

A vampire in a chador is the heroine of Amirpour’s first film, A Girl Walks Home Alone at Night. Made in Farsi and pristine black and white, the movie is set in an Iranian backwater called Bad City, a place of skeletal oil pumps, sweet tea and heroin. (The film was actually shot in the Californian town of Taft.) It is witty, romantic and authentically eerie, made with a stark post-punk prettiness. In the past few months, its success has seen Amirpour travel the world.

A Girl Walks Home Alone at Night trailer.

She tells the waitress she is beautiful. “I do that a lot now,” she says once the woman has left. “With boys and girls. It’s like, ‘Hey, move to LA – I’ll make you famous.’”

As a female director, and creator of a movie about a skateboarding vampire girl in a chador who ingests men, there have been questions from journalists about her sexual politics. The thought makes her wince.

“Am I saying something about women? Yes, and men, and children, and cats. If the film is feminist just because it’s about a girl who kills men, then maybe I am [a feminist]. But I also watch porn. Crazy gang-bang porn. I mean, I barely know what I am.” She looks exasperated, then suddenly brightens. “You know who’s a feminist? Lars von Trier. He’s the biggest feminist, and if I ever see that man I will run and jump and hug him.”

The girl is played by Sheila Vand, an Iranian-American actor who could pass for Amirpour’s sister. The mix of influences might seem unlikely: equal parts Iranian art movie and ode to US pop culture (Amirpour’s liking for vampires when she read Anne Rice novels as a child), with glints of spaghetti westerns and the nouvelle vague. Meeting her, it all starts to feel self-evident – a film that could only have been made by her.

Margate’s Dreamland amusement park. Photograph: Nicholas Bailey/REX Shutterstock

Amirpour was born in Margate. (She points this out with some excitement.) Her atheist parents fled Tehran in the first days of the 1979 Islamic revolution and arrived in Kent, where her father began work as a doctor. She recently went back there. “It’s depressing and post-industrial now but, at the time, I thought it was cool.” As an only child, she wandered the Dreamland amusement park, where performing monkeys clambered on her shoulder. Her parents, though grateful for the sanctuary, hated the weather.

When she was eight, the family left for Miami. “It was eighty ... five? Was I nine? Wait. Are you trying to figure out how old I am? I don’t want you to put my age in here.” She hesitates, and decides to explain. “I like to sleep with younger guys. And I look young ...” There is a small rustle of newspaper from the suited man at the next table.

Somewhere in her early 30s, Amirpour is still getting used to the art of interviews. “It’s hard to measure how much to give away. I’ve told my mother to stop Googling me.” Her conversation has its own rhythm; there are spikes of energy after a coffee, occasional moments of spaciness. She will, once or twice, pause her own answer to study a asserby. She is excellent company.

Miami was sunnier than Margate, but a culture shock. Amirpour arrived with a British accent that led her schoolmates to prod her into speaking on demand. “It wasn’t sweet. It was more like the Elephant Man.” A couple of years later, the family moved again – this time to Bakersfield, California, 100 miles north of Los Angeles. There, the “shrimpy brown kid” was widely assumed to be Mexican; Latino gang girls would occasionally threaten her for hanging out with white people.

The cape-like chador inspired Amirpour to make a vampire film. Photograph: PR

At home, the family spoke Farsi. She enthusiastically watched horror movies. (Her father, by then an orthopaedic surgeon, thought she was interested in anatomy.) But most treasured was a VHS of Michael Jackson’s Thriller – she watched the music video itself less than the accompanying making-of.

“I didn’t really have friends. I mean, I had a unibrow and I was awkward and I climbed trees. I was never girly enough to hang out with the girls with their berets and their soft hair. So I skateboarded and made things.”

Those things included spoof adverts and skits made with her father’s camcorder. Eventually, she rounded up enough peers for a slumber party and made them the cast of a slasher movie. When she showed the result to her parents, it made them jump. “That was very satisfactory.” She was 12.

Later, she became more adept socially, “and less interesting.” But the manic creativity continued. Her parents were delighted – as she was artistic, they said, she could become a plastic surgeon.

Amirpour at a screening of her film during Sundance Next Fest in 2014. Photograph: Frazer Harrison/WireImage

There was an attempt at medical training. It ended quickly. By the end of her teens, Amirpour was briefly living with a friend in the woods outside a snowboarding enclave in Colorado. When she returned to the grid, she moved to Los Angeles, went first to art school (“fun, but also an idle, dickhead thing to do”), then film school. She found solace in house music; dancing, she says, is still her favourite thing. Eventually, a short story she wrote attracted an agent who asked her to create a TV pilot. It was the first step into a day job making commercials, as her 12-year-old self once did for free. For an overnight success, she has “been working really fucking hard for years”.

The visit to Tehran in 2003 was her first. She says it was a rush to hear Farsi spoken everywhere, being surrounded by people who looked like her. But even in the chador, “they knew right away I was western – I keep my head up and I look you in the eye.” She gets angry talking about the mood of repression. “It’s a mess. Medieval. Suffocating.” How does it feel? “It feels like if I put my hand around your neck.”

Her film was always going to be set in Iran, shot in Farsi. She thinks of it as an Iranian fairy tale, and considers part of herself as Iranian, too. “But then I’m American. I’m very American.”

In her early 20s, Amirpour worked as a script reader for the production company of actor Tobey Maguire. It confirmed her suspicion that it was pointless to send off scripts to be read by an intern whose boss would never consider making your film. Instead, she posted the idea for her first film on crowdfunding site Indiegogo. Among those who donated the initial $57,000 (£37,500) was the novelist Margaret Atwood. A glorious photograph exists of Amirpour in a chador at Comic-Con with Atwood beside her wearing a set of vampire teeth.

“Making your first film,” she says, “you’re basically begging on the street. But sometimes a beggar draws a crowd, and that’s who I want to be.” There was a certain inevitability to the recent announcement that her next film, a “cannibal love story” called The Bad Batch starring Keanu Reeves and Jim Carrey, will be funded by the famously deep-pocketed Megan Ellison, backer of the likes of Paul Thomas Anderson and Spike Jonze.

“I want to explore my own brain,” she says. “I think I make films because I’m lonely. I’m just lonely, and it’s a way to try to tell the world who I am.” She spies someone interesting, her eye tracking them across the room. “That’s my right, right?

• A Girl Walks Home Alone at Night is released in the UK on 22 May