In a large saucepan, combine 2 cups of the milk and all the sugar. Heat over medium heat, stirring to dissolve sugar, until bubbles form around edge of pan.
Meanwhile, in a large bowl, whisk together remaining milk, egg, cocoa powder and cornstarch until smooth. While whisking briskly, gradually add hot milk mixture. Pour back into saucepan and cook, stirring constantly, for 8 to 10 minutes or until thickened (do not let boil). Remove from heat.
Stir in banana and vanilla. Serve warm or pour into a bowl, place plastic wrap directly on surface of pudding to prevent skin from forming and refrigerate for about 2 hours, until chilled.