There are lots of reasons why Ellie Kemper, the 38-year-old star of Unbreakable Kimmy Schmidt, first came to the attention of the show’s creators, Tina Fey and Robert Carlock. As Erin, the daffy secretary in the US version of The Office, for example, she turned a small role into an arresting comic showcase. And she was well known within Manhattan improv circles and had contributed pieces to the Onion and McSweeney’s. After five seasons of playing Kimmy Schmidt and with a possible movie in the works, however, Kemper is adamant that Fey’s original interest in her came exclusively down to her “big, pale face”.

It’s true, Kemper’s physiognomy has particular comic overtones. She is wide-eyed and almost manically sunny – “Oh my gosh! I love that question,” she says more than once – with a guilelessness so pronounced she imagines Fey taking one look at her and saying: “OK, thinking about her face, what could be funny? A cult victim!” (Kimmy Schmidt is the story of a woman released after 15 years of being imprisoned in a bunker by a doomsday cult leader.) In Kemper’s new memoir, My Squirrel Days, she describes herself as about as near to a jolly-hockey-sticks type as you can get in the US, the product of a wealthy St Louis family, who took pride in being great at PE and is not really interested in introspection. “I’ll be perfectly honest,” she says. “I signed on to write a book of personal essays and then I thought: ‘Oh my goodness, this is a very delicate task because how personal do I want to be? How deep do I want to go?’ And I realised I wanted to be entertaining and make people laugh – and I don’t want to reveal everything about my life in this book. The voice is a heightened version of me.”

And it is a fun read, similar in many ways to Fey’s Bossypants or Amy Poehler’s Yes Please, a kind of book-length piece of standup in which, once you get past the thin material of Kemper’s primary school years, she settles into a series of satisfying comic set pieces about brunch, Soul Cycle, her short-lived career as a hockey player and not washing her hands after she goes to the toilet at home. (An interesting debate by the way: is it disgusting? Why, if a limited number of people use your home toilet and your home is clean?) The closest the book gets to a long dark night of the soul is when her nascent comedy career seems to stall after a failed audition for Saturday Night Live and a standup performance that won a single laugh. In both cases, Kemper writes, she had bounced back by the evening.

Facebook Twitter Pinterest Tituss Burgess and Ellie Kemper in Unbreakable Kimmy Schmidt. Photograph: Everett/REX/Shutterstock

Yes, she says, she supposes she does have a quick-reboot mechanism, which puts her in mind of her father, “who whenever I see him at a low point, bounces back within hours. I don’t know what that is; a snapping-out-of-it mode? I would like to think I have that trait. It’s humiliating to have one person laugh at you in a show where you’re trying to be funny. Really awful. But what other choice do you have but to go on?”

As it happens, Kemper had lots of career choices; comedy was an eccentric direction for someone with her background, a graduate of Princeton and Oxford whose contemporaries, she writes in the book, all wound up doing things like becoming speechwriters for Obama. She is assiduous in mentioning the good fortune of her family – her father is a banker, descended from a line of bankers – so that “I am in a rare position in that my parents could help me financially. Not everyone has that luxury. But I didn’t put a time limit on [breaking through with her comedy] because I don’t how seriously you can take what you’re doing if you put a time limit on it. I don’t know if my parents thought differently, but I didn’t have a backup plan and I’m not trained to do anything else.”

During those early years trying to make it as a comedian in New York, she didn’t swan about like a trust-fund kid; if Kemper was subsidised, she also supported herself by auditioning for commercials and working in the now defunct cupcake shop Crumbs (where in spite of it being a main requirement of the job, she could neither remember what the cupcakes were called, nor what was in them). For many years, she struggled with the sense she wasn’t doing anything at all, an anxiety to which, even after the success of her roles in the Office and Kimmy, she is occasionally still vulnerable. “Most of my classmates were doing things where you go to an office – and there are very clear marks of achievement and progress that you don’t get when you’re pursuing an artistic path. So that was demoralising because you feel like you’re a bum. You feel like you’re still a teenager. For me, booking commercials helped, not only financially but also, ‘OK, I’m in a commercial … you can see this!’”

But, she says, “I still feel: ‘Do other people take my job seriously?’ Because it is a job – and it’s a job that you’re so lucky to have, but that also isn’t as structured as other jobs. You start to feel like: ‘Is this legitimate work?’ I remember one time saying I should be done with work at 5pm to my friend, a lawyer, and she was like: ‘Huh, work!’ And I was so mad because I was writing my one-person show. You have to start taking it seriously because nobody else will.”

Facebook Twitter Pinterest (Left) Kemper In her small but crucial role in The Office. Photograph: Chris Haston/NBC-TV/Kobal/Rex/Shutterstock

One thing she is grateful for: whereas the standup world is known to be horrifically macho, the world of improv theatre, which Kemper came up through in New York via Poehler’s group, the Upright Citizens Brigade, is a much more nurturing landscape because “improv is by definition a group performance and the central principle of it is: ‘Yes, and.’ The very best improvisers are not worried about the spotlight. They’re trying to serve the ensemble, which I think is a valuable life lesson. I never met a guy who thought: you’re not going to be funny because you’re a girl.”

Her biggest problem in those early years was getting any traction. It was winning the small role of Erin in the last two seasons of The Office that turned things around for Kemper, and brought her to Fey’s attention. She is still shocked – or rather, her default amazement flows on unabated – at the fact she not only won the title role in Kimmy Schmidt, but that the role was essentially written for her. “I’d like to think they saw a survival quality in this big, pale face, but I’ll never know. I do think part of it is that I’m not crazy, and working with someone who’s not crazy is always a plus.” She pauses. “I could be complimenting myself.”

In the show, she plays Kimmy with aggressive levity, a combination of hardcore whimsy and flashes of iron will that somehow combine to feel robustly feminist. The show operates at the level of urban legend – the fact that men don’t grow up worrying that someone is going to abduct them and keep them in a basement for 15 years but girls do – and as an expansion of victim representation; the humour, coming from within the tent, as it does, feels empowering.

Nonetheless, Kemper is well used to defending the show against the criticism that it mishandles a serious subject matter. “I was very worried when I heard the idea; I think it ran the risk of trivialising abuse,” she says. “But as soon as I saw the finished pilot script that Tina and Robert wrote, I realised, of course, these magicians handled it perfectly.”

The show also functions as a satire of how the popular press seizes on lurid abuse stories, and “it is so powerful to see the image of a person emerging from that [experience], not only intact but still determined and fierce. There’s a lot of strength in that.”

Facebook Twitter Pinterest ‘I wanted to be entertaining and make people laugh – and I don’t want to reveal everything about my life in this book. The voice is a heightened version of me.’ Photograph: Christopher Lane/The Guardian

In line with her experiences in the cake shop, Kemper turned out to be hopeless at learning lines. Her duties on The Office had been light and now she was carrying a show and, “I was amazed by my own inability to memorise scripts. I’d be like: Ellie, this is your job and you’re having trouble with it. I’m embarrassed to say it; it was just a new skill to master. But being the lead in a show is a totally different position. I remember thinking, oh, Steve Carell [who starred in The Office] must have been exhausted! It’s more responsibility. Then again, you’re an actor on a TV show that other people wrote.”

Her fan-girl adoration of Fey did not lessen with the experience of working with her – “Oh my gosh, I feel like never, ever could you take that for granted” – to the extent that when she delivered the first draft of her book, her editor suggested she might want to ease up on the Fey-worship. The fact is, she says: “I swear it was easier to memorise her lines than other lines. It just was. Because they’re so well written. I know that sounds like I’m kissing up to her, but there’s a rhythm to it. It’s effortless. She’s the funniest writer there is.” And she’s normal. “Everything I’ve ever seen about her is normal! She’s accomplishing all these things, but she’s so normal. I think she’s from outer space.”

Kemper is married to Michael Koman, a comedy writer on Saturday Night Live, and they have a two-year-old son, James, who is at the forefront of her mind as she considers her next move. “I would like to try to be in more movies,” Kemper laughs apologetically. “Doesn’t every actor want to? It’s hard with children.” One gets the feeling that, like Kimmy, she is a great deal steelier than her sparkly exterior suggests, or rather that her good cheer is an expression of fortitude. Beyond that, she says, it’s a choice. “What can you do if you’re not choosing to think that things will be OK?”

My Squirrel Days by Ellie Kemper is published on 4 October by Hodder & Stoughton.