In my recent YouTube listening, as I putter about my business, I've come across several delightful examples of musical theater songs, intended for male characters, being sung by women.
The first two of these are from MisCast, which I gather is an annual Broadway fest in which stars sing numbers they'd never be cast in a production for - although, especially in the first case, as the character has virtually nothing else to do in the show, I'd ask, "Why the hell not? She's really good!"
You may also, if you look under MisCast, find men singing women's songs, but I didn't find those as memorable, although, to be sure, Lin-Manuel Miranda and Raúl Esparza as Anita and Maria from West Side Story is a remarkable sight.
Carmen Cusack sings "You'll Be Back" from Hamilton. (Yes, the guy she taps on both shoulders with her scepter while coming on stage is Brian D'Arcy James. ETA: Who sang the part in the original off-Broadway production, so that's why he deserves to be knighted for it.)
Katrina Lenk sings "If I Were a Rich Man" from Fiddler on the Roof.
Linda Eder sings "I, Don Quixote" from Man of La Mancha.