Baby Face "The Beaver" Cleaver, is a gangster who works alongside his brother Wally Cleaver. He appears in the 1987 TMNT cartoon episode The Big Cufflink Caper! and is one of Big Louie's rivals. Big Louie asks the Turtles, who were trying to pass as mobsters, to prove themselves to him by putting Baby Face "The Beaver" Cleaver on ice.
Though the Turtles were uncomfortable with the mission, they ended up battling Baby Face and his goons. The fight spilled over into a mall next door, and particularly onto an ice rink where Baby Face attempted to kill the Turtles with a Zamboni machine. The Turtles managed to break the ice under the machine, and left him for the police to arrest.
He is a homage to the late 50's TV show "Leave it to Beaver" combined with a reference to real life Chicago mobster "Baby Face" Nelson.