Prepare cake batter according to package directions. If desired, adjust the cake mix instructions by adding one additional egg, double the oil amount, but use melted butter instead of oil, and use milk in place of the water. Divide batter between two greased and floured 9-inch round baking pans.
Bake at 350°F/175°C for 28-33 minutes, or until a toothpick inserted into the center comes out clean. May take longer to bake than box instructions. Let cool.
Whisk or beat the milk and pudding mix for 2 minutes. Let stand for 2 minutes or until soft-set. Cover and refrigerate.
In a microwave or saucepan, melt chocolate and butter over medium-low heat; stir until smooth. Stir in powdered sugar, vanilla and enough water to achieve a thick glaze; set aside.
To assemble, place one cake layer on a serving plate; spread with pudding. Top with the second cake layer. Spoon chocolate glaze over the top, allowing it to drip down the sides of cake. Refrigerate until serving.