This is "All Woman" — a song that was written by Lee Adams (lyrics) and Charles Strouse (music) for the 1960 Broadway show, Bye Bye Birdie Don't remember it? That's because it was dropped before the show ever got near Broadway and what you're hearing here is a composer's demo and that's probably Mr. Strouse singing it. Or maybe it's Mr. Adams. I dunno.
Most Broadway shows have cut songs and I've heard precious few that made me think, "Hey, that's a great song. I wonder why they cut it." This is no exception…