Unreadable. That word comes up frequently when producers talk about why they cast Carrie Coon: Onscreen, it’s hard to know what her characters are thinking.

That enigmatic quality has landed her two prominent roles this month — returning for the final season of HBO’s “The Leftovers” (premiering April 16) and starring in the third iteration of FX’s “Fargo” (April 19) as police chief Gloria Burgle, the latest in the series’ famed canon of female sheriffs.

But in person, Coon, 36, is anything but inscrutable. Warm, funny, and charmingly down-to-earth, she’s as stunned by her TV moment as anyone.

“I love Nora Durst so much, and she’s such a hard person to live up to,” she says of her character in “The Leftovers,” over midafternoon tea at the Culver Hotel in Los Angeles, on a rare, welcome escape from the “epically cold” set of “Fargo” in Calgary. “So the fact that I got to move on to ‘Fargo’ has blown my mind a little bit. I never thought I would have the opportunity to be on it.”

“Fargo” creator Noah Hawley cast her as his leading lady thanks to her “winning” ways. “There’s a positivity to her character as a person that comes through,” he says. “Obviously ‘The Leftovers’ is a very dark and emotional show with not a ton of hope to it, yet you always feel with her that she’s making the best of it. She’s going to figure it out.”

That tenacity was important to him as he charted out this season of “Fargo,” which finds Coon playing a character facing an ever-increasing set of challenges: a divorce, a difficult relationship with her 10-year-old son, and then, as Hawley says cryptically, “bad things happen.” And she has to cope with it all in that quiet, Midwestern way so characteristic of the FX series.

“My biggest dilemma with Carrie Coon as a director and writer is that I literally don’t have any notes to give her,” says Hawley. When he’s behind the camera, he admits he often simply instructs her to do another take just for the sake of doing it. “I’ve yet to find a flaw.” If “ ‘Leftovers” co-creator Damon Lindelof has found one, he adds, “Make sure you tell me.”

For the record, Lindelof can’t find one, either. The two showrunners exchanged texts when Coon was cast on “Fargo,” with Lindelof passing along high praise.

“It was so exciting for me as a fan of ‘Fargo’ and of Carrie to see what she was going to do next,” says Lindelof. “I was even more excited that ‘Fargo’ is an anthology series, and he can only use her for one season. Because then I’m going to come back after her.”

***

Coon says she’s rarely recognized by fans — indeed, we’re undisturbed throughout our lengthy conversation in the crowded restaurant.

She takes it as a compliment. “But when I am, it’s by someone who’s deeply connected to ‘The Leftovers,’ either because they were grieving or because they were going through a divorce or because they had never seen a female character quite like her expressed on television,” she says. “I’m really grateful for that. I’m grateful that that’s the kind of work I’m putting out to the world, that people can connect with on that level.”

Born and raised in Ohio, Coon found her way into acting via the stage. After touring the country in various regional theater productions, her performance in “Who’s Afraid of Virginia Woolf?” in 2012 marked her Broadway debut — and earned her a Tony nomination. She had a memorable role in 2014’s “Gone Girl,” and a few minor TV stints — including in NBC’s short-lived “The Playboy Club” in 2011 — but it was her self-taped audition for “The Leftovers” that grabbed casting director Ellen Lewis’ attention, and ultimately Lindelof’s and the rest of the HBO hierarchy. She was the first cast member signed, even before series star Justin Theroux.

“I remember something that J.J. Abrams said to me,” recounts Lindelof. “Which is, It’s good if you can cast great actors, but when it comes down to it, just cast people you want to hang out with. Carrie fortunately checked both boxes in a huge way.”

The third and final season of “The Leftovers” finds Nora still grieving the mysterious departure years ago of her husband and children — and yet still in some fragile relationship with Theroux’s Kevin Garvey.

“She’s redefining herself via her career, and it involves sensible pants,” teases Coon.

The actress has been well-trained not to reveal spoilers: “The difference is that with Noah, you get your scripts ahead of time, but you can’t talk about them,” she says. “And with Damon, you can’t talk about them because you don’t have your scripts yet.”

Following a quick time jump, circumstances will quickly propel the action from Jarden, Texas, to Australia for the rest of the season. Might it have something to do with her search for her family, who departed mysteriously in season one?

“One of the things we started to play with this year is, just because we as storytellers have said we’re never going to tell you where the missing people went or why, does that mean that Nora can’t try?” says Lindelof. “All that’s been missing for her is a lead or a clue. Now that we’ve given her something to chase, I think that that may have provided Carrie with some level of challenge. But when I watch what she did with it, she makes it look pretty easy.”

What Coon will reveal is that she’s going to miss Nora after “The Leftovers” comes to an end.

“She taught me so much about standing up for myself,” she says. “I very much feel that she, more than almost any character I’ve ever played, has become such a part of who I am now, moving forward.”

Still, Coon is ready to say goodbye to the enigmatic woman she’s embodied for three years. “I’d rather leave her when she’s still a little bit mysterious to me,” she says. “I can imagine a world where I would start to feel that Nora was retreading territory. And that maybe I was developing a Nora Durstian bag of tricks.” (Yes, she’s seen the crying memes on the internet.)

Lindelof recalls a pivotal scene from the first season, when Nora finds the mannequins of her family sitting around the kitchen table (they’ve been placed there by cruel cult members). “What was scripted was she lets out an inhuman wail,” says Lindelof. “That’s a very hard thing for an actor to do — act surprised when they’ve read the script and they know it’s coming. But still she came around that corner the first time, and she let out an inhuman wail. The hair on the back of my neck stood up.”

But for Lindelof, what was even more impressive was that Coon picked herself up off the floor and said matter-of-factly: “I can do three more of those.” “That noise had sucked all of the air out of the room, and that put the air back in,” he says. “That’s when I realized I was in the presence of a very unique artist.”

Theroux recalls knowing he’d met his acting match from Coon’s first day on set, when she had to deliver a powerful monologue about her departed children on a blistering hot day in New York City, even as extras were fainting around her. Three seasons in, his respect for her talents has only deepened.

“She’s beautiful at playing that duality: Completely fucked up, but also has this iron rod running from the top of her head to her heels,” he says. “I think it’s why she’s so enjoyable to watch. She comes off as soft at times, and dreamy. But then she has times when her body tenses and stiffens, and she’s absolutely terrifying.”

***

Coon has been an avid fan of “Fargo” since the first season. So when her name was first circulated for the cast, she could hardly believe it. “We’re very snobby about writing in our house,” she says. (Coon has been married to playwright Tracy Letts since 2013.) But Hawley’s oeuvre met her literary standards. “I was just immediately impressed by the sophistication of the writing and the female characters,” she says. “The women in that show felt like people; they didn’t feel like plot devices.” She rattles off a list: Allison Tolman, Kirsten Dunst, Jean Smart.

Coon points to the overall renaissance happening in television, especially for actresses of “a certain age.” “I think as more women get into producing and more female writers get the opportunity to have shows on the air — we all are benefiting from these incredible, complex women — that now we finally recognize women on TV,” she says. “They finally are starting to look like women we know in our lives.”

“Fargo” wraps in early May — “I’ll be free, if anyone’s listening,” jokes Coon — and she doesn’t have another project lined up. But she admits she’s picky.

“I don’t need to spend time doing something that doesn’t speak to my values,” she says, “because, inevitably in Hollywood, you play an FBI agent, and your next five offers are gonna be FBI agents. There’s a strange lack of imagination in an industry that’s supposed to be about creativity.”

Not so in the case of the award-winning “Fargo.” Stepping into the starring role as No. 2 on the call sheet — behind Ewan McGregor, who’s playing dual roles — hasn’t quite sunk in for her. She promises she’s still that same aw-shucks girl from Ohio.

“People keep telling me I’m in the position to ask for things and I haven’t figured out what those things are, and who to ask,” she says. “I’m not sure that’s good for anyone. My grandma Rosemary always puts her hands on my shoulders at Christmas and looks me in the eyes, and says ‘Good, you’re still the same.’ She’s very concerned about the pitfalls of Hollywood — and so far I’ve passed her test.”