In a large heavy saucepan, heat butter and water to boiling over medium-high heat. Add flour and reduce heat to low. Cook and stir until it forms a ball and pulls away from the pan. Remove from heat and transfer to a large bowl. Beat in eggs, one at a time, beating well after each egg.
Spread in bottom and up the sides of an ungreased 9x13 inch pan. Bake at 400 degrees F (200 degrees C) for 35 minutes. Cool completely.
To make the filling: In a large bowl, combine cream cheese and milk and beat until smooth. Here's the trick, to keep things smooth: start with the cream cheese, give it a good beating until fluffy. Slowly but surely (while still beating), add the milk. Voila! Once these are well combined, add pudding mix and beat until thickened. Spread over cooled shell.
Top with whipped topping, and drizzle chocolate syrup over the top. Keep refrigerated until serving.