Preheat oven to 400 degrees F. Grease 9x13-inch baking dish. Set aside.
In a medium saucepan, bring butter, water, and sugar to a boil over medium heat. Add flour and cook for 3 minutes, stirring constantly, until the mixture forms a ball. Transfer the dough to a large bowl.
Add eggs and beat with a hand mixer until fully combined. Spread the dough into the bottom of the 13x9-inch baking dish.
Bake for 35 to 37 minutes until the pastry is golden brown. The dough will puff up along the sides of the baking dish. Cool completely at room temperature.
Mix cream cheese and milk in a medium bowl until well blended. Add pudding mixes and beat for 2 minutes. Refrigerate until ready to use.
Spread the pudding layer over the cream puff crust just before serving. Top with Cool Whip.
Finely chop the chocolate then place it in a small microwave-safe bowl with the shortening. Heat on HIGH power for 20 seconds then stir well. Continue heating and stirring in 20-second intervals until it is completely smooth. Drizzle chocolate over the Cool Whip.