Make the vanilla pudding mixture: In a large bowl, whisk together the instant vanilla pudding mix and 3 cups of cold milk until smooth and thickened, about 2 minutes. Fold in the thawed whipped topping until well combined.
Layer the graham crackers: In a 9x13-inch baking dish, arrange a single layer of graham crackers to cover the bottom of the dish. Break the crackers as needed to fit.
Add the pudding layer: Spread half of the vanilla pudding mixture evenly over the graham crackers.
Repeat the layers: Add another layer of graham crackers on top of the pudding, followed by the remaining pudding mixture. Finish with a final layer of graham crackers on top.
Make the chocolate topping: In a medium bowl, whisk together the cocoa powder, powdered sugar, and milk until smooth. Add the melted butter and vanilla extract, and stir until combined.
Spread the chocolate topping: Pour the chocolate topping over the final layer of graham crackers, using a spatula to spread it evenly.
Chill the cake: Cover the cake with plastic wrap and refrigerate for at least 4 hours, or overnight, to allow the graham crackers to soften and the flavors to meld.
Serve: Slice and serve chilled. Enjoy the creamy, layered goodness!
