In a medium saucepan, combine sugars, cocoa powder, cornstarch, and espresso powder. Gradually stir in milk. Cook and stir over medium heat until thickened and bubbly; reduce heat. Cook and stir for 2 minutes more. Remove from heat.
Gradually whisk about 1/2 cup of the hot milk mixture into egg in a medium bowl. Add egg mixture to milk mixture in saucepan, stirring constantly. Return saucepan to heat. Reduce heat to medium-low; cook and stir for 2 minutes more. Remove from heat. Stir in butter and vanilla.
Place saucepan in a very large bowl half-filled with ice water. Stir pudding constantly for 2 minutes to cool quickly. Transfer to a medium bowl. Cover surface of pudding with plastic wrap. Refrigerate 2 to 24 hours. To serve, top with sliced banana and/or crystallized ginger. Makes 4 servings.