Preheat oven to 400F degrees. Prepare a 13x9-inch baking pan by lightly spraying with a non-stick cooking spray.
Add the butter and water to a medium saucepan and cook over medium heat. Once the mixture begins to boil, remove the pan from the heat and stir in the flour until the mixture forms a soft ball (use a wooden spoon for the best results).
Transfer the dough to a large mixing bowl. Prepare an electric mixer and have it ready to quickly beat in the eggs in the next step. Add the eggs one at a time, mixing thoroughly with an electric mixer in between additions (move quickly to begin mixing the moment you add the egg so it doesn’t cook on the hot dough). After all of the eggs have been mixing into the dough, continue to beat the dough on medium speed for 1-2 minutes until the mixture is smooth. Transfer the dough to the prepared baking pan and spread out evenly over the bottom. Tip: the dough is sticky, so it may help to use a spatula sprayed with a little non-stick cooking spray.
Bake for 20-23 minutes until puffed up the sides of the pan and golden brown. Remove from the oven and cool completely to room temperature (the sides may fall a little during the cooling).
In a large mixing bowl, use an electric mixer to beat the softened cream cheese until smooth, Slowly add 1 cup of the milk a little at a time, beating well in between each addition until the mixture is smooth (adding just a small amount of milk at a time helps prevent lumps of cream cheese).
Add remaining milk and the pudding mix and beat on medium speed for 2-3 minutes until smooth and thickened.
Spread the pudding mixture over the cooled crust, then top with the whipped topping.
Cover with plastic wrap and chill in the refrigerator for at least 1 hour (or overnight).
Drizzle with chocolate syrup before serving.