Like some crazed urban Peter Pan, Amanda Plummer is climbing up a fire escape ladder in high heels, her short skirt flying in the wind. A cup of coffee in one hand and a cigarette in the other, she’s heading toward the roof of a Beverly Hills office for a quick photo shoot. Suddenly, she appears to lose her footing, almost toppling to the pavement below. But oblivious to — or perhaps thrilled by — the danger, Plummer doesn’t whine like a spoiled starlet. Instead, the 37-year-old actress cackles impishly and continues to climb upward.

Perhaps it’s this on-the-edge attitude that inspired director-screenwriter Quentin Tarantino to custom-write a part for Plummer in his eagerly awaited “Pulp Fiction,” which opens the New York Film Festival this weekend. In it, she plays Honey Bunny, a small-time convenience store thief, who, along with her partner Pumpkin (Tim Roth), aspires to bigger things.

And maybe it’s this same determination that made director Roger Christian cast Plummer as the willful Catherine de Medici in the new movie “Nostradamus,” a dark tale based on the life of the famed 16th century prophet.

But whatever drew these directors to Plummer, doggedly moving on and up has always been her modus operandi. After several successful theater roles — “Agnes of God,” for which she won a Tony, “Pygmalion,” “A Taste of Honey,” “The Glass Menagerie,” plus an Emmy-winning performance for TV’s “Miss Rose White,” and an Emmy nomination for a stint on “L.A. Law,” she has found the road to big screen fame a rocky one.

While critics have consistently raved about her movie performances (Robin William’s lonely love interest in “The Fisher King,” a mute in “The World According to Garp,” a terrorist in “Hotel New Hampshire” and the tormented sister in “Daniel”), many of her films have gone largely unseen. Plummer is disappointed by the lack of leading roles that come her way.

Her father, actor Christopher Plummer (“Sound of Music”), and mother, actress Tammy Grimes, divorced when she was four, sending her into a private world of books and imaginary friends.

Even now, she’s no social butterfly. She arrives two hours late for her interview, casually puts on deodorant in the middle of her publicist’s office, then smokes like an exhaust pipe. On other days, she rollerskates through the grocery store, dances alone at nightclubs and has been known to shout obscenities to photographers mid-shoot.

“Sometimes, shocking behavior is a way to keep people at a distance,” notes Plummer slyly. “When I was young, I was ‘weird,’ then ‘crazy,’ and as I get older, it’s ‘eccentric.’ I like the sound of eccentric. It’s a lot better than being called boring.”

Unlike many New York transplants, Plummer doesn’t find L.A. a cultural wasteland. “I think L.A.’s funny,” she says. “All its contradictions are humorous. It’s like a toyland, yet it’s very real. It keeps you aware.”

Furthermore, it’s the place she met her current amore, writer-director Paul Chart, whose film “American Perfect” she’s set to start shooting in late November. “I’m in love,” Plummer confesses. “I met a man in the city where it’s impossible to meet men!”