Kirsten Dunst was 19 when a Spider-Man producer took her to get her teeth fixed. She didn’t know that was the plan – not until the car pulled up at the dentist’s office. Poised on the brink of stardom, preparing to play Peter Parker’s winsome love interest Mary Jane in the $130m comic-book adaptation, Dunst had everything producers were looking for: talent, youth, beauty. But wouldn’t that upside-down kiss look better with straight teeth? She didn’t get out of the car. “I was like, ‘Mmmmm, no, I like my teeth,’” says the 39-year-old now, her unaltered incisors crunching into a raw carrot. “Also, Sofia loved my teeth.”

Sofia Coppola, that is. When Dunst met the director, she had been working for well over a decade – she’d already had a creepy kiss with Brad Pitt in Interview with the Vampire, escaped an icy death in Little Women, and played the world’s most dangerous board game in Jumanji. But it was in the 28-year-old Coppola that she found her mentor. In the first of many collaborations, Coppola cast 16-year-old Dunst in The Virgin Suicides, a woozy fever dream of a film about five alluring yet tormented sisters. There’s a certain innocence projected onto women who look like Dunst – blonde hair, blue eyes, pin-prick dimples – and as the rebellious Lux, she took that and twisted it into something deeper, darker. It was a skill she’d deploy many times in the years that followed.

Coppola – who just this year described Dunst as “the top actress of her age” – took the teenager under her wing. “The fact that the coolest girl liked how I looked, that’s what preserved me,” says Dunst now. “She made me feel pretty. As a 16-year-old girl, you feel like crap about yourself, right? So to have my first experience of a more ‘sexy’ role be through her eyes gave me a confidence that helped me deal with a lot of other things.” Had it been a male director complimenting her looks… “Totally different!” she interjects. “You’d be like, ‘Ew, don’t say that, I’m 16.’”

Spider-Man was a far cry from the arthouse intrigue of The Virgin Suicides, but Dunst brought that same knowing glint to a character who could have been little more than a cipher. The film brought in $821m, its sequel $789m. Dunst didn’t see much of that. “The pay disparity between me and Spider-Man was very extreme,” she says. “I didn’t even think about it. I was just like, ‘Oh yeah, Tobey [Maguire] is playing Spider-Man.’ But you know who was on the cover of the second Spider-Man poster?” She flashes a grin and points at her chest. “Spider-Man and ME.”

Dunst is like a lit-up circuit board; she speaks quickly, eagerly, as if she has news she’s been dying to tell you. When she greets me, in the depths of a swanky London hotel, her first words are “Look at us!” because the pattern on her black-and-white dress is not dissimilar to that of my jumpsuit. She’s a little jet-lagged, she tells me, taking a seat next to a big plate of raw veg and dip, but it’s nice to have the bed to herself after months of “doing the nights” with the new baby. Her two boys, Ennis and James, are back home in Texas with her fiancé, Jesse Plemons, who happens to play her husband in the film she’s here to discuss: Jane Campion’s beautiful, austere frontier drama The Power of the Dog. “I was full on for a good five and a half months and then I was like ‘Byeeeee!’” she says with a laugh. “I mean I miss them, but it has been nice to not be like, ‘Oh is that my sweat or did he pee in the bed?’ You know what I mean?” No, not really. “Oh, well get ready! It’s so tiring.”

Anyway, back to the teeth. Does Dunst think she’d have got into that dentist’s chair had she never met Coppola? “Who knows? I mean, I have a really good mom, too, but my mom is someone who might have been like, ‘Yeah, why not have straight teeth?’” Dunst’s mum recently conceded to her daughter that she was “too vain” when she was younger. “I just remember her wanting to get a face lift or a boob job, those kinds of things. It never looked good. That kind of vanity… you’ve got to be really careful with that stuff.” She laughs. “It made me reject it more, I guess.” So on the poster for Spider-Man, Mary Jane’s teeth were magically straightened, and Dunst’s “snaggle fangs” lived to see another day.

It was a fitting decision for an actor who trades in imperfection – who rejects the glossy artifice of Hollywood while still operating within it. But if there’s one thing that unites her performances, it’s that their genius tends to only be recognised years later. The cult teen movie Bring It On? She brought both edge and peppy charm to head cheerleader Torrance, but the film’s critics couldn’t see past the pom poms to the sharp satire on white privilege. The pitch-black mockumentary Drop Dead Gorgeous? She was gamely tragic as a tap-dancing pageant hopeful brawling with her rivals. The critics hated it, and then changed their minds somewhere down the line. Even Sofia Coppola’s Marie Antoinette, a lavish, anachronistic delight and one of Dunst’s finest performances, was sneered at – and yet so many recent period dramas feel like they owe something to that film. “I couldn’t agree with you more,” says Dunst, with such vehemence that she bursts out laughing. “Maybe if a male director had directed it, it would have been [better received]. I think maybe people were threatened by Sofia too, in a way.” At the time, she couldn’t help but blame herself. “I thought we made something special, and then everyone kind of… didn’t feel that way. You’re like, ‘Oh, what did I do?’”

She was even egregiously overlooked, by awards bodies if not critics, for Lars Von Trier’s Melancholia. As a newlywed hit with such all-consuming depression that her food tastes “like ashes”, she gives a performance so crushingly visceral, you can almost taste the ashes yourself. She should have won an Oscar for that, but she wasn’t even nominated. Nor has she ever been. The Oscars, the Golden Globes, the Baftas – Dunst has been overlooked so often that in a viral interview a few years ago, she wondered aloud what she had done wrong.

She looks a little embarrassed when I mention that, but she stands by the sentiment. “I did feel a little like, ‘Huh, I’ve been doing this for so long. Maybe I’m just not…’” She pauses, then decides not to go down that road. “I’d rather carve out my own career path than follow some kind of formula. I’d rather be in that crew.” After doing Melancholia, for example, she “only got offered roles where the women were depressed” – so she made the raucous comedy Bachelorette instead. “And now I’ve worked with Jane Campion. I’m just fine. I’m not worried. I’m not complaining at all.”

Whisper it, but The Power of the Dog might just be the one to break the curse. In Campion’s first film in 12 years, Dunst plays Rose, a timid woman living in 1920s Montana, trampled under the heels of society and circumstance. The owner of a lodging house frequented by drunks, Rose is a “suicide widow” – as Benedict Cumberbatch’s brutish cattle rancher Phil so callously puts it. The two first meet when Rose’s son Peter (Kodi Smit-McPhee) – a quiet, feminine boy who crafts paper flowers and disembowels rabbits with equal care – is bullied by Phil while he serves him supper. When Phil’s pointed cruelty brings Rose to tears, it is his meekly benevolent brother George (Plemons) who comforts her. Soon, Rose and George are married, but living under Phil’s roof gradually erodes what little sense of worth Rose had to begin with. She turns to the bottle.

Dunst didn’t exactly enjoy stepping into the shoes of someone so deeply insecure. The dynamic between Rose and Phil, one filled with noxious micro-aggressions, felt “like having a controlling boyfriend”, she says. “It’s like, ‘How did he do that to me?’ You’re just so surprised by what you can let someone do to you. So for me as an actress, going to all those old feelings was a really painful place to live in. I don’t want to be insecure. It’s a very old part of myself that I had to re-hash. It would even make me question my acting. It was not a fun place to be every day.”

When you’re a little girl talking to older men, it’s a weird dynamic

Kirsten Dunst

When she was younger, “I never stood up for myself or said anything back. Even just saying no and knowing your worth, that’s such a big deal.” She corrects herself. “It’s not that big of a deal. Guys have been doing it forever.”

Were those old insecurities made worse by being an actor in the public eye? “I don’t think it’s an actor thing…” She thinks for a moment. “I definitely had a controlling boyfriend at one time. But it’s also like, when you’re a little girl, and you’re talking to all these older men, and doing press, it’s a weird dynamic.” I mention an old interview I dug up on YouTube, with an uncomfortably tactile David Letterman. She is 13, and he is probing her about her on-screen kiss with Brad Pitt, when she was 10 and Pitt was nearly 30. “Was this the first time you’d kissed a boy in a film? Was it odd?” he asked her. “I forgot about that interview,” says Dunst now. “Yeah, that’s weird. Why was that OK?”

Things are different now, of course, especially for young girls – but how would she feel if her boys wanted to go into the industry as young as she did? “Then my kid would already be working,” she scoffs. “My three-year-old would already be doing, like, kid modelling.” Dunst’s first gig was a cereal advert when she was three, which led to a contract with Ford Modelling Agency. She has mixed feelings about being put through that so young. “I judged it a lot more before I had kids. I was like, ‘How could you do this to us? Who puts their children in… you know, whatever.’ But when you have a cute kid and everyone’s like, ‘Oh my God, you should take them in to do little kid modelling,’ I get it. It’s fun.’”

She takes out her phone and pulls up a video of Ennis on his first day of school. There he is, hair as blond as the Milky Bar Kid’s, two huge dimples like his mum, arms stretched out as far as they can reach. “He’s literally doing jazz hands! I mean, listen, he definitely has some theatrics in him. I was picking him up from his little school and he was the only kid who ran out and was like” – she does a melodramatic gasp – “‘Mommy!’ It’s so sweet but I was also slightly embarrassed.” She laughs. “When your kid acts like that, you would think, ‘Oh this kid needs to be seen. Let’s try it. He seems like he would be into it, and we’ll just put the money away for college.’ I could see how that could happen. More so than ever.”

Besides, I say, most parents wouldn’t predict that their kid’s going to end up extremely famous, being grilled by Letterman about kissing Brad Pitt. “Yeah! It’s a snowball effect. And I clearly enjoyed it. And I’m still doing it.” She shrugs. “I love doing it.”

‘The Power of the Dog’ is out in UK cinemas on Friday 19 November. It will be available on Netflix from 1 December