Stir together egg and sugar in a large saucepan; gradually stir in milk. Cook over medium heat, stirring constantly, 18 to 20 minutes or until mixture thickens and coats a metal spoon.
Remove from heat; stir in brandy, rum, and vanilla. Cover and chill 8 hours.
Beat whipping cream at high speed with an electric mixer until soft peaks form; fold into chilled egg mixture.
