In a large saucepan, bring water and butter to a boil. Add flour all at once and stir until a smooth ball forms. Continue beating until smooth and shiny. Remove from heat and let stand for 5 minutes. Add the eggs one at a time, beating well after each addition. Put in a greased 9x13 baking dish. Bake at 400 degrees for 23-26 minutes or until puffed and golden brown. Cool completely on a wire rack. Don't worry if it puffs way up above the dish, it will shrink down as it cools.
For the filling, in a large bowl, beat the softened cream cheese, milk, and pudding mixes until smooth. Spread over the crust. Refrigerate for 20 minutes. Spread with Cool Whip. Chill until serving.