Prepare the pudding mixture:
In a large bowl, whisk together the vanilla pudding mix and cold milk until thickened.
Gently fold in the whipped topping until smooth and creamy.
Layer the cake:
In a 9x13-inch baking dish, arrange a single layer of graham crackers to cover the bottom.
Spread half of the pudding mixture evenly over the crackers.
Add another layer of graham crackers, followed by the remaining pudding mixture.
Finish with a final layer of graham crackers.
Add the chocolate frosting:
Slightly warm the frosting in the microwave for about 10–15 seconds to make it spreadable.
Spread the frosting evenly over the top layer of graham crackers.
Chill and serve:
Cover the dish with plastic wrap or foil and refrigerate for at least 4–6 hours, preferably overnight.
Slice into squares and serve chilled.