Bake cake mix according to package directions for 2 (9-inch) round cake layers. Cool completely. Use 1 of the cake layers as directed below. Wrap up remaining cake layer and store in the freezer for up to 1 month.
Cut cake horizontally into 2 thin layers with a serrated knife. Stack cake layers on a serving plate.
Whisk together pudding mix and 1 cup of milk for 2 minutes. Stir in Cool Whip. Let stand 5 minutes. Spread pudding mixture between layers.
Microwave chocolate and butter on high for 1 minute, stir until chocolate is melted. Add sugar and 2 tablespoons of milk, mix well. Spread over top of cake only. Refrigerate 1 hour and serve.