“Polkadots and Moonbeams” is a Jimmy Van Heusen, Johnny Burke composition published in 1940. Frank Sinatra had the first hit with it with the Tommy Dorsey Orchestra. It’s been widely covered including by Bob Dylan on his 2016 album Fallen Angels.
This version by Mel Torme appeared on his 1955 album Its a Blue World.
According to William Ruhlmann at AllMusic, Tormé invested the songs [on this album] with warmth and confidence. Recorded and released around the time he turned 30, It’s a Blue World marked a turning point in Mel Tormé‘s recording career.