Danny Kaye (born David Daniel Kaminsky) was an all-around actor, comedian, and musician, and something of an overachiever in all three areas; he seems to have been something of a workaholic, since he was always juggling multiple projects. In 1945 and 1946, he did a variety show for the CBS radio network, The Danny Kaye Show; it became very popular, very quickly, but it didn't last long because of the host's busy schedule!
"Valentine to Jack Benny", from February 10, 1945, gives a good mix of the kind of antics one found on the show. Since the show usually specializes in goofiness as its particular brand of humor, mileage will vary, but there are some solid guests -- Eve Arden, for instance -- and it has my very favorite Danny Kaye song-skit, one of the great classic comedy songs: "Stanislavsky", which was written by Sylvia Fine, his wife.
You can listen to the show at Internet Archive. If you're pressed for time, you can listen to just the Stanislavsky skit on YouTube.
And, for no other reason than that everyone should hear it at least once, here is perhaps the one Danny Kaye song that is more famous than "Stanislavsky": "Tchaikovsky" (written by Ira Gershwin, and originally entitled "Tschaikowsky"), which names a number of famous Russian composers. Kaye tried to sing it faster everytime he sang it; they had to start doing it a capella because the orchestra couldn't keep up with him.