Preheat oven to 400º. Lightly grease a 9"x13" glass baking pan.
For the Crust:
In a medium saucepan, melt butter in water and bring to a boil. Remove from heat. Stir in flour. Mix in one egg at a time, mixing completely before adding another egg. Spread mixture into pan, covering the bottom and the sides evenly. Mixture will be very wet.
Bake for 30-40 minutes or until golden brown. Remove from the oven and let cool (don't touch or push bubbles down). Let cool in fridge.
For the Filling:
Whip cream cheese in a medium bowl. In separate bowl make vanilla pudding by beating the pudding mix and the milk for 3 minutes and put in the fridge until set. Make sure pudding is thick before mixing in with the cream cheese. Slowly add pudding to cream cheese, mixing until there are no lumps.
When the crust is completely cooled, pour filling in.
Top with a layer of cool whip, however thick you want it.
Drizzle the top with the Chocolate syrup.