Preheat the oven to 400 degrees fahrenheit.
In a medium saucepan, heat the butter and water together until butter is completely melted and mixture boils. Add all of the flour and mix with a wooden spoon for 30-60 seconds until mixture forms a ball. Remove from heat.
Transfer dough into a mixing bowl and beat with an electric mixer on low for about a minute until it's not too hot to touch anymore. Then beat in the eggs, adding one egg at a time and beating on low until it's fully incorporated.
Spread dough onto the bottom and up the sides of an ungreased 9x13 glass pan. It doesn't need to be smooth. Bake for 25-30 minutes until crust is nicely golden brown.
Allow the crust to cool for 15-20 minutes.
Place the cream cheese, milk, and vanilla in a blender and process until smooth. Add the instant vanilla pudding mix and pulse four or five times until incorporated. The mixture will begin to set up quickly.
Pour the pudding mixture into the crust and smooth the top. Spoon Cool Whip or whipped cream over the pudding and smooth it out. Drizzle chocolate sauce over the top if desired OR drizzle sauce on individual pieces as you serve.
Cover cake with plastic wrap and chill until ready to serve. If you'd like to serve right away, put it in the freezer for about 15 minutes to help everything set up.