On a December morning in Los Angeles, the sun blazes down on a large and abundantly decorated Christmas tree in the parking lot at Paramount Pictures. It is upstaged, though, by the actor Taraji P Henson, who swans past wearing an ensemble that calls to mind the futuristic fashion of the 1970s: steampunk sunglasses, a black tracksuit under a puffy gilet and chunky grey, orange and lime sci-fi pumps, possibly with rocket boosters in the soles. Her hair is arranged in tight braids, some piled on her head, others swishing around her shoulders.

As we take our seats in a brightly lit office upstairs, she removes from her flowery backpack a tub of beige mush. What is that, mashed banana? “Nuh-uh,” she says between mouthfuls. “It’s an oatmeal alkaline thing. It’s got quinoa in it. I gotta be careful because I don’t digest a heavy grain.” She takes a sniff and laughs. “It smells like dirt, it really does.” She went vegan last year after a doctor told her it could reduce the chances of getting stomach cancer. “You can do it if you have a good chef,” she says encouragingly. I make a mental note to have a chat with mine.

From anyone else, that remark might have sounded impossibly pompous. But Henson, who is 48, has the informality and downhome directness that is to be expected from someone raised on the breadline in Washington DC. Her best roles draw on that natural earthiness in different ways. As the music industry matriarch Cookie Lyon in five series of the hip-hop soap opera Empire, she is brassy and brash. As Queenie, who cares for the elderly in The Curious Case of Benjamin Button, she is deeply tender. As Katherine Johnson in Hidden Figures, one of the groundbreaking African American women working at Nasa who helped put John Glenn into orbit, her humility amplifies the character’s achievements. And much of the charm in What Men Want, her broad and exuberant new romp, comes from her eagerness to act the giddy goat.

She had been in the business for two decades when she won a Golden Globe in 2016 for her work in Empire. Even longer if you count her presence as an extra in Spike Lee’s Malcolm X in 1991 as the real beginning of her screen career, long before films-in-the-hood such as Baby Boy and Hustle & Flow. “Me and my girlfriend were, like, ‘Denzel’s gonna spot us!’ Now why in the hell would Denzel Washington notice us? They had a thousand extras. We were like pepper specks! Nah, that was me saying to myself: ‘One day, I’m gonna be on the Denzel side of things.’” And now she is. Success, though, was a long time coming. As she put it when someone off-stage signalled for her to curtail that barnstorming Golden Globes acceptance speech for her performance in Empire: “Please wrap? I waited 20 years for this. You gonna wait!”

Don’t forget that she had also been up for a best supporting actress Oscar for Benjamin Button in 2009, six years before Empire came along, and even that nomination led mainly to films of only negligible impact (Date Night, The Karate Kid, the Tom Hanks flop Larry Crowne). Somehow, the defining role she needed kept eluding her.

With Aldis Hodge in What Men Want. Photograph: Jess Miglio/Paramount Pictures

“I don’t think Hollywood quite knew what to do with me. They didn’t grasp my talent. I’m like a musician. Give me the sheet music and I’ll play you anything.” I ask what she has in mind and she starts snatching ideas from the air. “I wanna play a wizard! A warlock! Put makeup on me. Make me a long-nosed witch, some Harry Potter fantasy thing. Take me out of my body. Make me fly. Put me in a muscle suit, a mask, put me in a – I don’t know – a fatsuit. I’ll play Jabba the Hutt. I’ll play anything!”

In that period between Queenie and Cookie, Henson was all set to star as a pregnant sex worker in the comedy St Vincent. The director, Theodore Melfi, had created the part specially for her; Bill Murray would play her grumpy alcoholic chum. But while Melfi may have written the screenplay, Harvey Weinstein was signing the cheques. The producer vetoed her and hired Naomi Watts for the role instead. In a racetrack scene in the finished film, one of the horses is named Harvey Knows Best, which may or may not be sarcastic.

Was Weinstein’s decision a matter of race? “Yeah,” Henson says. “Basically, I don’t think he saw my box-office appeal. What I heard – I didn’t sit down with the man – is that he wanted someone who was known internationally, so they got Naomi Watts.”

How does she feel about his subsequent downfall? “Well, you know, I just sit here and I sip my tea.” A sly smile appears as she does just that. “I never wished anything bad on the man. I was just, like, ‘OK, he’ll see. That’s another person who’ll have to eat crow. How would you like yours? Fried? Toasted?’”

The way she views it, she might never have been cast in Hidden Figures, Melfi’s follow-up, if she hadn’t met him for St Vincent. “That’s how God works. He had a bigger plan.” Now her career looks very different. Or, as she puts it: “I call the shots.” When she hosted Saturday Night Live in 2015, she began her monologue by telling the audience: “This proves, after 20 years in the business, that white people finally know who I am!” But then it had always been her ambition to appeal to as wide an audience as possible. She had often told her son, Marcell, that she wanted to reach beyond the black community. “Then after Baby Boy, a white couple came and spoke to me in a shopping mall. My son was all cool about it, but afterwards he said: ‘Mom! Mom! They weren’t black!’”

What Men Want is the sort of vehicle that only stars get to make: precision-tooled and shaped to the lead’s precise specifications. Coming in the aftermath of Weinstein and #MeToo, it is nothing if not timely. Henson plays a high-powered sports agent who is unfairly overlooked for promotion in favour of a junior male colleague. Her problem, she is told, is that she relates poorly to men. But after her tea is spiked by a fortune teller (the joyfully cuckoo Erykah Badu), she finds she can hear men’s innermost thoughts as clearly as if they were broadcasting them on loudspeaker. It’s a gender-switched spin on What Women Want, the 2000 comedy in which the chauvinist who gains new insights into the opposite sex is played by (oh dear) Mel Gibson. Repurposing it now with an irrepressibly sexual African American woman seems like a fitting act of detoxification.

As Cookie Lyon in Empire. Photograph: Chuck Hodes

Henson claims she has already witnessed the effect of #MeToo on her workplace. “It’s all handshakes and stiff arms from guys on set now. Me, I don’t take any of that stuff personally. I can laugh at anything.” In fact, her sense of humour has limits. A year ago, she fired her longtime manager, Vincent Cirrincione, following widespread claims of sexual misconduct against him from young female actors. “We’ve all been through painful things and my defence mechanism is usually to laugh. To beat you to the punch. I’ll laugh at me before you can do it. But catch me on the wrong day and I’ll be like: ‘Bitch, what you say?’”

What Men Want is important, too, in exploiting Henson’s underused knack for slapstick, pratfalls and mania. She learned from the best. “I used to stand in front of our old tube TV as a child, watching Lucille Ball, studying everything she did. I had to be that close to the screen to see exactly how she stomped on the grapes and what faces she pulled, so that I could mimic her. Comedy was my escapism because I lived in the hood.” Adam Shankman, the director of What Men Want, knew that Henson’s mastery of physical comedy would be central to the movie. “I wanted her to approach the part very physically because the movie felt to me like an extremely fast-paced slamming-door farce,” he says. “Also we had a low budget and so I knew Taraji was going to be my special effect. She has this encyclopaedic knowledge of old screwball comedies. I could say to her, ‘Now I need you to be like Rosalind Russell in His Girl Friday’ or whatever, and she could just pull it out of the hat.”

Henson points out that comedy was her original calling; it’s what she first came out to Los Angeles to do. One sitcom part followed another before she made a splash as Tyrese Gibson’s long-suffering girlfriend in Baby Boy. “And that was that. Suddenly I was a serious, dramatic actress and people stopped calling me in for comedies, even though I tried to put some funny into everything I did.”

It is as Cookie, a riotous cocktail of Almodóvar matriarch and blaxploitation badass, that she has really had the chance to show her range. The moment she left prison in the pilot episode and announced: “Cookie’s coming home”, it was clear she would be to Empire what James Gandolfini was to The Sopranos, albeit with snazzier threads. From her parole outfit of white fur, clingy leopard-print dress and hoop earrings big enough for a dog to leap through, it has been a constant battle to see which would be the more outrageous – her wardrobe or her behaviour.

“I thought one of my movies would make me a star,” she says. “Not Cookie, who beats her kids with a broom and went to jail for selling crack. Wow. OK, people, that’s what you want?” She thinks the clue to the character’s popularity is her frankness. “She’s all about living your 100% truth.” Could there ever be an Empire without her? “I don’t think so. You kill her off, you’ve killed the mama. What would the boys do without her?”

With Empire co-star Jussie Smollett. Photograph: Brad Barket/Getty Images

When I call her three months later, she is in Chicago, where she lives most of the time with her fiance, the former NFL player Kelvin Hayden, and where she is currently on set shooting the sixth season of Empire. She draws a blank when I remind her that we spent an hour together before Christmas (“We did?”), then charmingly makes amends: “Well, it sure is nice to talk to you, uh, again.” And when I tell her I’ve just seen the new film, she seems momentarily confused – “Um, I’m sorry, which film are we talking about?” But that’s understandable: in the midst of shooting Empire, she is also promoting not only What Men Want but also The Best of Enemies, in which she stars as the civil rights activist Ann Atwater, who forged an unlikely friendship with the Ku Klux Klan leader CP Ellis, played by Sam Rockwell.

Besides, a lot has happened since our last meeting. In January, Henson got her own star on the Hollywood Walk of Fame. “I still can’t believe it,” she says during a break on set. “When people mention it, I’m like, ‘Oh yeah, that happened.’”

In the same month, her Empire co-star Jussie Smollett, who plays one of her sons, claimed he was the victim of a hate crime in Chicago. Two men bombarded him with racist and homophobic abuse, then hung a noose around his neck. Last month, the case took a strange turn when Smollett was arrested on suspicion of staging the attack and filing a false police report.

“Jussie’s gonna be just fine,” she says soothingly when I enquire after him. “He’s my sweetheart. I believe him. He’s a victim and he needs to be treated like one.” After we speak, Smollett was charged with filing a false report and could face one to three years in prison.

And only this week, Henson has been lashing out on social media at anyone who criticises The Best of Enemies based on the trailer alone. “They haven’t even seen it!” she splutters. “They just seen me with a white guy in the trailer and they’re projecting all this stuff on to it. Don’t do that! I’m so annoyed. I’m an artist so I’m sensitive about my shit.”

Could this discord about yet another unlikely black/white friendship be connected to the frustration about Green Book winning best picture? “Probably. That’s what I felt it was,” she says.

When I ask if she voted for that film, her response is perfectly diplomatic. “The one I loved was If Beale Street Could Talk. And Bohemian Rhapsody. Look, I was happy for Green Book. Octavia Spencer [one of its executive producers] is a dear friend, and Mahershala Ali is a dope actor.”

Could she understand those who were bothered by the movie? “I guess I can. It maybe feels like the same formula – the white saviour and all that. People are getting tired of the story being told in that way.”

So, will the reign of the old, rich, white man ever come to an end, as What Men Want suggests it could? “I don’t think it’ll come to an end, but there’s room for all sorts of stories, and Hollywood is finally seeing what’s needed. Look at Crazy Rich Asians. I loved that movie. The people on screen might not look like you, but so what? Everyone needs representation. And if the movie’s good, and it has heart, that’s all that matters.” She’s being called back to set now: our time is up. “Empire is waiting for me,” she laughs, all too aware that everyone wants a bite of Cookie.

What Men Want is out next Friday. The Best of Enemies is released this year.