Combine water and butter in a saucepan; heat until boiling. Whisk in flour until smooth; remove from heat. Pour mixture into a medium bowl; gradually blend in eggs.
Spread in a greased 13"x9" baking pan; bake at 350 degrees for 30 minutes. Remove from oven; press baked crust down lightly and set aside.
With an electric mixer on medium speed, beat together cream cheese, milk and pudding mix for 2 minutes; spread over crust. Refrigerate until firm.
At serving time, spread with whipped topping; drizzle with chocolate syrup.