“I have a wonderful disappearing cloak,” Amy Adams tells me. “It’s to do with shortness. And I can be quite homely when I take my make-up off.” I suppose that’s possible. Strip away the accoutrements of celebrity and even the most luminous star can seem flesh and blood. But there would be no mistaking Adams today. Everything about her gleams with health and warmth. For all the supposed “ordinariness” that characterised breakthrough roles, Adams still wields the charisma of a golden-era movie star.

As I enter, Amy is staring suspiciously at a snot-coloured smoothie thing. “There are a lot of greens in there,” she says suspiciously before sipping. “Who’d have thought it? I do love this, but it really does taste of grass.”

The Month of Adams November is the Month of Adams. Last week, she appeared as an emotionally stricken art gallery owner in Tom Ford's extraordinary Nocturnal Animals. From today, you can see her as a linguist – commissioned to open communications with visiting aliens – in Denis Villeneuve's even better Arrival. It's the sort of intelligent science fiction we rarely see in the enormoplex these days. I do hope people will see it.

“I think people are hungry for this sort of film,” she says. “It’s sneaky. It has that element of science fiction there. Then it asks people to think. My niece and nephew saw it and what they liked about it was the science. I knew my mom would have questions.” She pauses to chuckle.

“Actually, my mom is the only person I’ve taken to the film who hasn’t cried. I was like: ‘Come on, mom?’ And she said. ‘Oh I know, but it was you up there and I just like to watch you act’.”

I’m not sure what sort of accent Amy is doing in her impersonation of Mom. Like a great many Americans, the younger Adams is from a whole bunch of places. As a younger person, she lived in Colorado and Minnesota and Virginia. Am I allowed to refer to her as an “Army brat”? He dad was serving overseas when she was born.

“Ha ha! Yeah, that’s okay. I was a brat. I was born in Italy. Then we moved to Virginia and Colorado. I guess I say I’m from Colorado. I’m a Colorado girl.”

Adams's career has a peculiar structure. Having secured five Oscar nominations for a tasty variety of parts, she now comes across as Hollywood royalty, but fame came in a peculiar series of fits and starts. A significant role in Steven Spielberg's Catch Me If You Can, released in 2002, looked likely to cement her position, but it didn't quite happen. It was another three years before Amy's turn in Junebug secured her an unexpected Oscar nomination. Yet it was not until 2007 and a lead role in Enchanted – incandescent as a princess adrift in New York – that Adams secured her seat at the high table. This is a woman who spent three whole years doing dinner theatre in Minneapolis.

“Look, I was just bad at everything else,” she says. “I am a horrible waitress. I hadn’t pursued anything else. I had to see this through. I definitely explored things. I went to New York and tried a stage career. I worked enough to keep me in the business. I never thought ‘oh, it is so hard being an actor’. This is my choice. Nobody is making me do this.”

Do the sums. Adams was into her 30s before she became properly famous. That may go some way to explaining her almost supernatural composure and relentless good manners. Then again, she has always acknowledged the firm old-fashioned values that her parents instilled. One of seven children, she was raised in the Mormon Church and feels that its teaching helped instil discipline.

“I always tried to live way below my means,” she says. “Anyway, the point is I stayed with it. I was in class with actors who were stunning and opportunity never came for them. I was aware that opportunity came for me. And it came repeatedly. So, I was able to say: I am on the right course.”

She goes on to say that she would audition for absolutely everything. If the job paid she would go for it. So, come on, Amy. Own up to the most embarrassing role. There must be some humiliation awaiting disinterment.

"Oh I got all sorts. But I loved every one," she laughs. "Everything has been unearthed. It's all there. I remember when I was doing Catch Me If You Can, Leo (DiCaprio) said: 'I was watching Cinemax last night and I came across you behaving very poorly with a teacher.' And I was like: 'Oh yeah – Cruel Intentions 2?' It's all out there."

The success in Enchanted could have come at a price. Adams was so good as the perky ingénue – a role played by Doris Day in earlier times – that typecasting loomed as a present danger. We allow ordinary mortals to carry around all kinds of contradictions, but movie stars are supposed to fit within their package. Adams really is as open and unpretentious as those early perky roles suggested. She has, however, worked hard to manoeuvre her way into divergent paths. She is brassy in David O Russell's The Fighter. She is determined in Tim Burton's Big Eyes. She is positively sinister in Paul T Anderson's The Master.

A common thread "My blind belief that I wouldn't fall into that kept me from falling into it," she says. "For a while people were saying my characters in Doubt and Miss Pettigrew were all the same. 'You really think those girls are alike?' I'd say. Maybe there's a common thread of naivety, but if you are looking to see typecasting, you can find that in anyone's career. I always had faith that wouldn't happen."

She credits David O Russell with bolstering that confidence.

"He got The Fighter and, based on a conversation we had about something else, he said he wanted me to play this role. 'You want me to play a girl who gets in a fight? That's awesome!' That really helped."

Adams manages an admirable balance in her public life. She is not any sort of recluse. Indeed, journalists clamber after her when she arrives at the red carpet. But, married to artist Darren Le Gallo, whom she has been dating for 15 years, she has made no noisy appearances in the tabloids. Their six-year-old daughter has been allowed to live a normal existence.

“I am hoping changes in the law have helped those things a bit,” she says. “They are not supposed to be harassing children. I don’t bring her to events. It’s difficult. She’ll ask to go. How do you explain to a six-year-old that the press then feels a degree of ownership?”

She sighs. "There's this notion: if you didn't want attention then you shouldn't have brought her to the red carpet. I'm aware of that attitude. If I take her to the premiere of Trolls then they can photograph her at dance class. That's the logic, apparently."

A rare shadow passes across the Adams visage. I am reminded of Susan, her depressed, anxious character in Nocturnal Animals. Susan looks with horror at a version of the LA nightmare she helps sustain: vacant, narcissistic, amnesiac. It's hard to imagine Amy having any part of that.

“Oh, I have avoided that stuff altogether,” she says, “so I can’t really give you an insider’s view, but I always fear with a series of different choices I could have ended up like Susan: very removed from my authentic self.”

She has another slug of squashed grass. “It’s always good to remind myself to stay close to what’s in my heart and not to follow my fears.”