Once upon a time in New York City, two young talents set off on a near-impossible quest: a successful Broadway career. Since childhood, Idina Menzel and Kristen Bell had focused on their quest with a ferocious drive — and learned to avoid the trolls.

In Long Island, Menzel, the daughter of a pajama salesman, spent her weekends singing at weddings and bar mitzvahs, and otherwise kept her big voice a secret. “No one knew how good I was at school because I didn’t want kids to know,” admits Menzel today. “I didn’t want to be the one to show off.”

Meanwhile in Michigan, Bell signed up for every community play and helped support her single mother by modeling underwear and karaoke machines for Kmart catalogs. Classmates would brandish shots of her in a training bra. Bell didn’t care. That money would get her to Manhattan.

Both Menzel and Bell arrived at New York U.’s Tisch School of the Arts and began to audition. Menzel got to town a little earlier, and the very first gig she landed was the original Broadway production of “Rent.” Her full-throated performance as the sexually fluid performance artist Maureen earned her a Tony nomination — in part thanks to her cocky delivery of the line, “There’s always going to be women in rubber flirting with me!” — and icon status among theater fans who obsessed over the soundtrack. One of whom was Bell.

“She was such a young queen,” Bell says. “She was so powerfully inspiring when I was studying music and theater at NYU.”

Menzel made success seem easy. After “Rent,” she inaugurated the role of the resentful green-skinned Elphaba in “Wicked,” which won her that Tony, and spun her Broadway smashes into thematically adjacent roles in movies including “Kissing Jessica Stein,” “Enchanted,” the film version of “Rent,” and, of course, “Frozen.”

Even Menzel’s disasters were spun into gold, as when she fell through a trapdoor during the melting scene of her next-to-last performance of “Wicked” and cracked a rib, forcing her to cancel her final show. That night, Menzel put on a track suit and swallowed enough pain medicine to walk onstage during the closing bows. Her show of strength made national headlines, including a farewell salute in the New York Times.

“You have no choice! That’s just what you do!” says Menzel. As for that time John Travolta flubbed her name during the Oscars, that, too, became a blessing. “It ended up being this really wonderful mistake that helped ingratiate me to people. Anyone that didn’t know me knew me now, and anyone that did know me was more supportive.”

“It’s hard to go unnoticed when you sing like Idina,” Bell says. To most people, Menzel’s career seems a string of mega-hits, as though, like her fantastic characters Elphaba and snow queen Elsa, she was born with a superpower she simply had to harness. To her, however, the fairytale story has crumpled pages.

“If you look at the time in between those jobs, they’re close to a decade,” Menzel says. “In those off-times, I have gotten very insecure and felt that I couldn’t get a job, and was dropped from record labels, and had to go on many an auditions that I didn’t get. Having a career that goes up and down has made me really appreciate when I do have success. I know the real deal — the days where nobody is calling and you feel like crap.”

As for Bell, she, too, found success fast. Bell scored her first Broadway gig as Becky Thatcher in “The Adventures of Tom Sawyer” before she could graduate college. A year later, she was onstage alongside Liam Neeson and Laura Linney in a revival of “The Crucible.”

“I have always been a hustler,” says Bell. “I’ve been really, really, really lucky that at the times I was available and ready to audition, someone was in need of a 5’1” blonde with a little bit of quirk.”

Bell had always planned to spend her career on the stage. Yet, now that she was a 22-year-old Broadway veteran, Bell began to think about a trip she’d taken to Los Angeles when she was 14. Though money was tight, her mother had agreed to fly her precocious daughter to meet a Hollywood agent. She and her mother walked down Hollywood Boulevard to look at the stars, and Bell was struck by how many names she didn’t recognize.

“I was taken aback by the sheer number of people that have contributed to the arts here,” Bell says. “It made me realize how many artists there are in the world.”

She chose to stay committed to finishing high school and studying theater in New York. But when her L.A.-based co-stars in the Off Broadway production of “Reefer Madness” urged her to join them in California, on a whim, Bell decided to see if her happily-ever-after was on the other coast.

“I definitely heard from numerous adults in my life that cared about me, ‘Have a backup plan, have a backup plan, have a backup plan.’ But I also heard from some other artists, ‘If you have a plan to fall back on, you’ll fall back,’” says Bell.

“So I just decided to go for broke — I’ve always been an optimist.” Within a week, Bell booked a guest spot on “The Shield.” Within a year, she was cast as the lead on “Veronica Mars.”

Still, even after proving she could charm audiences in every genre from crime-fighting teenagers to bitter comedies (“Forgetting Sarah Marshall,” “Bad Moms”) and cerebral sitcoms (“The Good Place”), Bell was nervous when she finally met Menzel.

“I’d always looked up to her,” Bell says. “You could never have convinced me that the first time I would meet her would be at her house to practice a duet to present to Disney executives after the ‘Frozen’ reading.”

The two spent an afternoon perfecting a duet of “The Wind Beneath My Wings,” the ultimate ode to sisterly love. Finally, Bell admitted that it felt surreal to sing in person alongside a voice she’d known so intimately on tape.

“She was incredibly gracious,” says Bell, “but also looked at me in a way that was like, ‘OK, you can be excited, but also, we’re trying to get this job, so let’s do the work.’”

On audition day, they sang the Bette Midler mega-hit while staring deeply into each other’s eyes. At the end, according to “Frozen” director Jennifer Lee, the entire room was misty-eyed. Yet Bell says she and Menzel burst into giggles at the absurdity of sharing this big moment in a generic boardroom. “And then,” says Bell, “we went on this crazy eight-year adventure together.”

“Frozen” became the highest-grossing film of 2013, raking in more than $1.2 billion worldwide, and it won Oscars for animated film and original song, thanks to Menzel’s showcase “Let It Go.” In the past six years, the property has snowballed into books, costumes, toys, theme-park rides, Norwegian tours, holiday specials, ice skating shows, and, of course, live musical theater. And on Nov. 22, Disney is releasing “Frozen 2,” the same week that Bell and Menzel will receive stars on the Hollywood Walk of Fame in a joint ceremony. That’s harmony.

The two girls who dreamed of making it on Broadway will now have their names engraved into Los Angeles’ Hollywood Boulevard. It’s a little ironic, but the timing is apt — particularly for Menzel, whose dramatic turn as a jilted wife in the Adam Sandler thriller “Uncut Gems” is one of the year’s best surprises — and one in which she doesn’t sing a note.

“I want to push myself in all different directions. It’d be fun to let people see the other side of the Disney princess — or queen,” she corrects herself. “There is a more raw, quote-unquote, uglier side that I would not be afraid to show.”

In that spirit, Bell has a pitch for Menzel when the two are octogenarians: a musical version of “Whatever Happened to Baby Jane.” “That would be a nice way to go out, right?!”

“I love that she’s got us booked when we’re 80!” laughs Menzel when she hears of Bell’s plans. “I’d like to figure out what we can do two years from now, but that’s cool!”