Nicole Kidman just revealed she was once engaged to rocker Lenny Kravitz, telling The EDIT that she was quietly betrothed to the father of her Big Little Lies costar Zoë Kravitz years ago. The actress and musician dated in 2003, and PEOPLE covered their under-the-radar romance in this vintage cover story below:

One thing you can say for Nicole Kidman: The woman knows how to keep a secret. Throughout the summer, the Oscar-winning actress dismissed inquiries of a romance with rocker Lenny Kravitz with “we’re-just-friends” denials. Yes, she was renting his apartment, but please don’t get the wrong idea. Meanwhile, the two befuddled photographers by arriving and exiting hot spots around Manhattan at separate times. A coincidence, naturally—celebs often stumble over each other at the coolest places. Over the weekend of Sept. 19, however, the couple popped up at several high-profile events, including a tribute to Gregory Hines at the Apollo theater. The buzz increased accordingly.

Then, on Sept. 30, the pair finally came clean: Kidman had indeed fallen for her leather-trousered landlord. Reps deny reports that the couple are engaged but won’t discuss persistent buzz that the two will announce an engagement in the near future. “They’re very close,” says her spokeswoman Leslee Dart. “He’s very important to her. Beyond that, I don’t know.”

In retrospect, a romance between Kidman, 36, and Kravitz, 39, was in bloom to anyone who saw them together at an intimate dinner party at Tavern on the Green on Sept. 13 or at magician David Copperfield’s birthday party at Tao restaurant six days later or at Kidman pal Naomi Watts‘s birthday bash at the hip Tribeca eatery 66 on Sept. 25. “They were always touching each other,” says one Tavern on the Green witness of the “flirtatious” demeanor that’s grown since Kidman (in town shooting the big-budget comedy The Stepford Wives, costarring Matthew Broderick) first sublet the rocker’s SoHo digs while work continues on her own $8 million West Village apartment. Adds another: “They were gazing at each other all night long. She was sitting on his lap, massaging his leg. They were eating off each other’s plates.”

And not just because she preferred his salmon to her filet mignon. Though the actress and rocker, who met through a mutual friend, appear to be an odd couple, they share more than an affinity for music and Manhattan. For starters, both are single parents: Kidman to Isabella, 10, and Connor, 8, from her 10-year marriage to Tom Cruise that ended in 2001; Kravitz to daughter Zoë, 14, with ex-wife and former Cosby star Lisa Bonet, 36.

2013 CMT Music Awards - Red Carpet
Credit: Kevin Mazur/WireImage

Both are family-oriented: Kidman counts her mother and sister among her closest friends and brought her father and kids to Watts’s birthday party last week, while Kravitz, the only son of NBC news producer Sy Kravitz and the actress Roxie Roker (who played Helen Willis on the ’70s sitcom The Jeffersons) named his recently launched recording company after his mother, who died in 1995.

Most important, perhaps, both are open to romance. “I’m not so much looking for the one as waiting for the one,” Kravitz said last year. In April, meanwhile, Kidman spoke candidly of her “very single” status to PEOPLE. “It’s lonely when you know you don’t have someone in your life to protect you,” she said. “I want someone who says, ‘I will stand by you and be there for you, and your life is just as important to me as mine.’”

So has she found that someone? Born in Brooklyn, Kravitz grew up on Manhattan’s Upper East Side in a close-knit and artistically vibrant household. Frequent houseguests Count Basie and Duke Ellington awoke his musical side, while his mother turned him into a fashion maven. As he said, “She had all the cool clothes in the closet that I used to go play with when I was a little kid.”

When he was 11, his family moved to L.A., where he recoiled from the rich-kid culture of Beverly Hills High School (“I saw how destructive money can be,” he said) and focused on teaching himself to play guitar, keyboards, bass and drums. At 16, he began his musical career with the stage name Romeo Blue—complete with blue hair and contact lenses. By the time he won his first Grammy (out of four) for his hit song “Fly Away” in 1998, the blue was long gone, but Romeo was alive and well.

After his six-year marriage to Bonet ended in 1991, Kravitz was linked to a string of high-profile beauties including Madonna (with whom he cowrote the 1990 hit single “Justify My Love”), model Naomi Campbell and singers Kylie Minogue, Natalie Imbruglia and Vanessa Paradis. But the swinging single life got tougher when Zoë started having a say. Living with him for the past few years (his main residence is in Miami), she is “very protective,” he told PEOPLE in 2001. “She screens my dates big-time. She wants someone for me who’s real and sincere.”

The protectiveness is mutual. According to Kravitz’s friend, interior designer Benjamin Noriega-Ortiz, Kravitz is “a great dad. His daughter could easily have been very spoiled, but she’s just like a regular girl.” (Not counting the guitar, bass and drum lessons he gives her between chores.) “He’ll reprimand her when she does something wrong. But he’s also quick to say something nice.”

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A hands-on parent like Kidman, Kravitz also shares with her a love of clothes. She is known for a free-spirited couture style, Kravitz for a funky beatnik look now accented by jewelry of his own making—though as he says, his daughter doesn’t find him as cool as the rest of his fans do: “I’m just her dad, who needs to shave sometimes.” Filial eye-rolling notwithstanding, Noriega-Ortiz, who worked extremely closely with Kravitz on his SoHo penthouse duplex, says that Kravitz has a special way with all things creative—from writing music to decorating. “He likes designing everything,” says Noriega-Ortiz. “He’s very concerned with the emotion of a room. Everything is love and peace and sensual. His home is both his sanctuary and a place for inspiration.”

Just the place for a great romance—or a low-key evening watching reruns of The Jeffersons, as Kravitz likes to do, with his daughter and a special someone. At Tavern on the Green, Kidman made clear her affection not only for Kravitz but for Zoë, who accompanied the pair. “She was very good with her,” says an observer, “friendly and speaking to her a lot.” A week later, it was grown-ups only at Copperfield’s lavish 47th-birthday party. “They held hands, whispered in each other’s ears, were basically cheek-to-cheek the entire time,” says one eyewitness. “They looked like a couple.”