1Process milk and banana in blender or food processor until smooth.
Mix sugar and corn starch in medium saucepan; stir in milk mixture. Heat to simmering over medium heat, stirring occasionally.
2Lightly beat egg yolks in small bowl; whisk about 1/2 cup milk mixture into egg yolks. Whisk yolk mixture back into saucepan. Cook over medium heat, stirring constantly, until thick enough to coat the back of a spoon. DO NOT BOIL!
3Remove from heat, stir in rum, liqueur and vanilla. Pour into large heatproof pitcher or bowl.
Cover; refrigerate until chilled.
Just before serving, stir half and half into eggnog mixture. Serve in mugs or punch cups; garnish with dollops of whipped cream and sprinkle of cocoa.