Heat the oven to 400°F and lightly grease a 9 x 13-inch baking dish.

Place the water and butter in a saucepan and bring them to a boil. Remove the saucepan from the heat, add the flour all at once, and stir until a smooth ball forms and the dough pulls away from the sides.

Let the dough cool for about 5 minutes. Beat in the eggs one at a time, mixing thoroughly after each addition.

Spread the soft dough evenly in the prepared baking dish. Bake for 25–30 minutes, until puffed and lightly golden, then cool completely.

Beat the softened cream cheese, powdered sugar, and vanilla until smooth. Spread this mixture over the cooled crust.

Whisk the two pudding mixes with the cold milk for about 2 minutes, or until thickened. Spread the chocolate pudding over the cream cheese layer.

Spread the thawed whipped topping over the pudding. Drizzle with chocolate syrup if desired, then cover and refrigerate for at least 1 hour before serving.