Mix the Filling: In a large mixing bowl, whisk together the instant vanilla pudding mix and the cold milk until well combined and the mixture begins to thicken. Gently fold in the thawed whipped topping until smooth and fluffy.

Build the First Layer: In a 9x13-inch baking dish, arrange a single layer of graham cracker squares to cover the bottom. Break the crackers into smaller pieces as needed to fit the edges and completely cover the bottom.

Add the Pudding: Spread exactly half of the vanilla pudding mixture evenly over the bottom layer of graham crackers.

Second Layer: Arrange a second layer of graham crackers directly on top of the pudding mixture.

Add Remaining Pudding: Spread the remaining half of the pudding mixture evenly over the second layer of crackers.

Final Cracker Layer: Top with a third and final layer of graham crackers.

Initial Chill: Cover the baking dish securely with plastic wrap and place it in the refrigerator for 30 to 60 minutes to allow the pudding to firm up slightly.

Prepare the Frosting: Remove the lid and all of the foil seal from the tub of chocolate frosting. Microwave the open tub for about 15 seconds until the frosting is softened. Stir well until it reaches a smooth, easily spreadable consistency.

Frost the Cake: Remove the cake from the refrigerator and pour the softened frosting over the top layer of graham crackers. Spread it into an even layer using an offset spatula.

Final Chill: Re-cover the dish with plastic wrap and return it to the refrigerator. Let it chill overnight (or for at least 8 hours) so the graham crackers can fully soften into a delicate, cake-like texture.

Serve: Slice into squares while cold and enjoy! Tip: For an even firmer slice, place the cake in the freezer for one hour prior to cutting.