Prepare the vanilla pudding: Whisk the instant vanilla pudding mix with 4 cups of cold milk for two minutes until slightly thickened. Let it stand for five minutes.
Fold the thawed whipped topping into the pudding mixture until fully combined.
Prepare the graham crackers: Pour 1 cup of cold milk into a shallow dish. Quickly dip each graham cracker sheet into the milk for about one second per side. Do not soak them too long.
Assemble the first layer: Arrange a single layer of the dipped graham crackers on the bottom of a 9×13 inch baking dish.
Spread half of the pudding mixture evenly over the graham cracker layer.
Add the second layer: Place another layer of dipped graham crackers on top of the pudding.
Spread the remaining half of the pudding mixture over the second cracker layer.
Add the top layer: Place a final layer of dipped graham crackers on top of the pudding.
Spread the chocolate frosting evenly over the top layer of crackers.
Chill the cake: Cover the dish and refrigerate for at least 6 hours, or preferably overnight, before slicing and serving.
Notes
For a richer chocolate topping, warm the store-bought frosting slightly before spreading it on the cake.
You can use chocolate instant pudding instead of vanilla for a more intense chocolate flavor throughout.
Make sure you dip the graham crackers very quickly; over-soaking makes them fall apart.