In a large bowl, whisk together cold milk and instant pudding mix until smooth and thickened.
Fold in the whipped topping gently until fully combined.
In a 9x13-inch baking dish, arrange a single layer of graham crackers on the bottom.
Spread half of the pudding mixture evenly over the graham crackers.
Add another layer of graham crackers on top.
Spread the remaining pudding mixture evenly over the second layer.
Top with a final layer of graham crackers.
Microwave the chocolate frosting for 15–20 seconds to make it spreadable, then spread evenly over the top layer.
Cover and refrigerate for at least 6 hours or overnight before serving.