Inside Out Cream Puff Cake

For the Eclair Dough
1 cup water
1 stick butter
1 cup all purpose flour
Pinch of salt
1 cup eggs (about 4 large eggs)

For the Filling
1 (3.4-ounce) package French Vanilla instant pudding mix, plus ingredients called for on the pudding package
1 (8-ounce) container whipped topping

For the Chocolate Sauce Topping
3/4 cup milk
1/4 cup butter at room temperature
Pinch of salt
1 cup sugar
1/4 cup cocoa powder
1 tablespoon cornstarch
1/2 teaspoon vanilla

Eclair Dough:
Combine water and butter in a 4-quart heavy saucepan and bring it to a simmer. Once the butter has completely melted, add the flour and stir will, then continue to stir over medium heat for 2 minutes. It is important to cook it the entire 2 minutes so that the flour will cook completely. The dough will stick to the sides of the pan and then form a ball keep stirring and cooking.
After 2 minutes, remove from the heat and place dough in bowl of an electric mixer. Allow to cool about 5 minutes. Then, with the machine running on low, add the salt and eggs one at a time with time in between each addition. The dough will change in appearance from looking like scrambled eggs to a shiny batter. Continue to beat for about 2 minutes until it pulls away from the bottom or sides of the bowl.
Spread the dough into a greased 9 x 13-inch baking dish, pushing it into the corners and up to the sides.
Preheat oven to 425 degrees F and bake for 15-18 minutes. It should no longer look wet and should look lightly golden brown.
Return the pan to the oven with the heat off, leave the door ajar and allow to cool to room temperature.
Assembly:
Make the pudding according to package directions and chill. May be used immediately or chilled, covered up to one day before assembling cake. Thaw whipped topping in the refrigerator for 4 hours before assembling cake.
After the base has cooled completely, spoon prepared pudding into the center, smoothing evenly and pushing to the edges. Top with the whipped topping, again smoothing evenly and swirling in a decorative pattern. Drizzle with about 1/3 cup of the chocolate sauce. Cover cake lightly with plastic wrap and chill for 1 hour before serving.
Chocolate Sauce Topping:
In a 1-quart saucepan over medium high heat, combine milk, butter, and salt and bring it to a boil. Combine the sugar and cocoa powder and stir to get rid of any lumps, then add to the pan and continue to stir with a whisk until it boils and is thickened, at least 2 minutes.
The mixture should coat the back of a spoon when thickened. It will continue to thicken as it cools.
Remove chocolate sauce to a small bowl and cover and chill 1 hour before using. Sauce can be stored in the refrigerator up to a week. Bring to room temperature and stir before using.