Preheat the oven to 400 degrees F (200 degrees C).

Combine water and butter in a large, heavy saucepan over medium-high heat; bring to a boil. Add flour and reduce heat to low; cook and stir until forms a ball and pulls away from the pan. Remove from heat; transfer to a large bowl. Beat in eggs, one at a time, beating well after each addition.

Spread dough into bottom and up the sides of an ungreased 9×13-inch baking dish.

Bake in the preheated oven for 35 minutes. Remove from the oven; set shell aside until completely cooled.

Beat milk and cream cheese together in a large bowl with an electric mixer until smooth. Add pudding mix; beat until thickened. Spread over cooled shell. Top with whipped topping; drizzle with chocolate syrup.