In a large bowl, whisk together the instant vanilla pudding mix and the cold milk until thick, about 2 minutes.
With a rubber spatula, fold in the whipped topping until well combined and smooth.
Line the bottom of the baking dish with a layer of graham crackers, breaking pieces to fit the dish as needed.
Spread half the pudding mixture over the graham crackers.
Add a second layer of graham crackers.
Spread the remaining pudding mixture over the second layer of graham crackers.
Add the third layer of graham crackers.
Remove the foil lid from the frosting and microwave for 10 to 15 seconds until the frosting is easy to pour.
Pour the frosting over the top layer of graham crackers and spread it over the top.
Cover the pan with plastic wrap and chill for at least 8 hours or overnight.
Slice and serve cold.