Prepare the Pudding Mixture: In a large bowl, whisk together the instant vanilla pudding mix and cold milk. Stir until smooth and thickened, about 2 minutes.
Add the Whipped Topping: Gently fold in the whipped topping until fully combined, creating a creamy filling.
Layer the Graham Crackers: Start by placing a layer of graham crackers at the bottom of a 9x13-inch pan.
Spread the Pudding Mixture: Spoon half of the pudding mixture over the graham crackers, spreading it evenly.
Add More Crackers: Repeat the process with another layer of graham crackers, followed by the remaining pudding mixture.
Final Layer: Top with another layer of graham crackers, ensuring the pudding is completely covered.
Make the Chocolate Icing: In a small bowl, mix melted butter, cocoa powder, powdered sugar, and milk together until smooth. Spread the icing over the top layer of graham crackers.
Chill: Cover the cake with plastic wrap and refrigerate for at least 4 hours or overnight for best results.
Serve and Enjoy: Slice into squares and serve this delightful cake chilled!