Mix the Pudding: In a large mixing bowl, whisk together the instant vanilla pudding mix and 3 cups of cold milk. Follow the package instructions for the pudding to set; this usually takes about 5 minutes.
Fold in Whipped Topping: Gently fold in the thawed whipped topping into the pudding mixture until well combined.
Layer the Cake:
First Layer: Arrange a single layer of graham crackers at the bottom of a 9×13 inch baking dish. You might need to break some crackers to fit the dish perfectly.
Pudding Layer: Spread half of the pudding mixture over the graham crackers evenly.
Repeat Layers: Add another layer of graham crackers over the pudding layer. Then, spread the remaining half of the pudding mixture over the second layer of graham crackers.
Final Layer: Finish with a final layer of graham crackers on top.