Prepare the vanilla pudding according to package directions, substituting the required amount of milk with cold milk. Let it sit for 5 minutes to thicken slightly.

Gently fold the thawed whipped topping into the thickened pudding mixture until fully combined.

Arrange a single layer of graham crackers on the bottom of a 9×13 inch baking dish. You may need to break some crackers to fit the edges.

Spread half of the pudding mixture evenly over the layer of graham crackers.

Add a second layer of graham crackers on top of the pudding.

Spread the remaining half of the pudding mixture over the second layer of crackers.

Top with a final layer of graham crackers.

Spread the entire can of chocolate frosting evenly over the top layer of crackers.

Cover the dish tightly with plastic wrap.

Refrigerate for at least 6 hours, or preferably overnight, to allow the graham crackers to soften completely.

Slice and serve cold.