In a large mixing bowl, whisk together the vanilla pudding mix and cold milk until thickened. Fold in the whipped topping until smooth and fluffy.
Arrange a single layer of graham cracker squares on the bottom of a 9x13-inch baking dish. Break crackers if necessary to fully cover the surface.
Spread half of the pudding mixture evenly over the graham crackers.
Add another layer of graham crackers, then spread the remaining pudding mixture on top. Finish with a final layer of graham crackers.
Remove the lid and foil from the chocolate frosting container. Microwave for about 15 seconds, then stir until spreadable.
Spread the frosting evenly over the final layer of graham crackers.
Cover the dish with plastic wrap and refrigerate for at least 8 hours, preferably overnight.
Slice into squares and enjoy a chilled, creamy, chocolate-covered dessert.
