In a large mixing bowl, whisk together the instant vanilla pudding mix and cold milk until smooth and thickened, about 2 minutes.
Gently fold in the whipped topping until fully combined.
In a 9x13-inch baking dish, arrange a layer of graham crackers on the bottom.
Spread half of the pudding mixture over the graham crackers, smoothing it out evenly.
Add another layer of graham crackers on top of the pudding mixture.
Spread the remaining pudding mixture over the second layer of graham crackers.
Top with a final layer of graham crackers.
In a small bowl, mix the chocolate frosting with 1 tablespoon of milk until it reaches a pourable consistency.
Pour the chocolate frosting over the top layer of graham crackers, spreading it evenly.
Cover the dish with plastic wrap and refrigerate for at least 4 hours, or overnight for best results.