Adam Lambert Covers Cabaret’s ‘I Don’t Care Much’ in New Music Video (Exclusive)

Adam Lambert is putting his spin on one of musical theater’s most-treasured tunes.

The superstar singer is currently treading the boards as the mysterious Emcee in Cabaret at the Kit Kat Club, director Rebecca Frecknall’s acclaimed revival of the landmark 1966 musical currently running at the August Wilson Theatre in New York City. And in a move to mark both the milestone of his Broadway debut and the power of this production, Lambert has recorded a cover of “I Don’t Care Much,” John Kander and Fred Ebb’s haunting Act II ballad.

“This is probably my favorite song to sing in the show,” Lambert, 42, tells PEOPLE in a phone conversation to discuss the song, which is streaming now in a release via The Orchard. A music video for the single, filmed on location at the Kit Kat Club, was released early on Friday, Dec. 6, too.

“I’m really proud of it,” he adds. “There’s a timelessness to this song. It’s so beautiful …