Allison Janney's Dad Is Finally Impressed with Her Career Thanks to “Palm Royale” Costar Carol Burnett (Exclusive)

The Oscar winner stars as a colorful, 1960s socialite in the new Apple TV+ comedy

Allison Janney vividly recalls visiting her grandmother on Long Island as a child and watching her sashay around her beach club.

“She would wear cigarette pants and have a big straw hat and her shaker of martinis with her lady friends, who were very well-appointed and definitely had money,” the actress, 64, tells PEOPLE. “I just remember thinking, ‘Am I ever going to be like that?’ ”

Janney gets her chance—and then some—with her colorful new role as a self-appointed queen bee among 1960s socialites in the Apple TV+ series Palm Royale, launching March 20. It’s just another in a long line of characters the star has masterfully inhabited over the years.

From films like Juno, The Help and I, Tonya—which earned her a Best Supporting Actress Oscar win—to beloved TV series such as The West Wing and Mom, Janney has an uncanny ability to find a character’s “vulnerability, what’s really underneath all the bravado and the exterior shell of jewelry and makeup and hair and clothing,” as she puts it. “And that’s what’s exciting, to find that dichotomy there to bring to life.”

Despite all her accolades, Janney insists it’s her current gig as Evelyn Rollins co-starring alongside veteran actress Carol Burnett that got one particular family member's attention. “It was just so much fun to be a part of this world that our set designer created,” she says of the show. “We had the pointy bras; all the underpinnings were what women really wore during that time."

And not to mention, the cast. "I mean, Carol Burnett literally was the reason I wanted to be an actress," adds Janney. "My father now believes my career is legitimized because I’m working with her. It’s the first time he was like, ‘Wait, what?’”

Janney recalls first becoming curious about acting after watching her mom, who had been an actress. “She had been roommates with Eileen Brennan and Rue McClanahan. And so I was very much aware of that being an option for me,” she says.

“I did a lot of plays in school as well. But when I got to New York and really tried in earnest to be an actress, I found it very hard because I’m so tall, and it took me a long time to get off the ground,” she says. “I did a lot of Off-Off-Off-Broadway theater and auditioning and quitting and coming back. It was a lot of lean times for me.”

As for being recognized, the actress jokes it’s been more “thinking I was being recognized when I wasn’t,” she says. Once when she was riding on the subway, “I thought, ‘Gosh, everyone’s looking at me. I must be getting too famous to ride on the subways.’”

When she got up to leave at her stop, "I looked down and my shirt was completely unbuttoned to my waist," she recalls. "So it was more of my bra and chest hanging out. I was like, 'All right, let's calm down.'"

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Palm Royale is now streaming on Apple TV+.

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