Prepare the Pudding: In a large bowl, whisk together the 2 packages of instant vanilla pudding mix and 3 cups of cold milk until smooth. Fold in the 8 oz of whipped topping until fully combined and creamy.
Assemble the Layers: Arrange a single layer of graham crackers in the bottom of a 9×13-inch baking dish. Spread half of the pudding mixture over the graham crackers, smoothing it out evenly.
Layer Again: Add another layer of graham crackers on top of the pudding mixture. Spread the remaining pudding mixture over this layer and top with a final layer of graham crackers.
Make the Chocolate Topping: In a small saucepan over low heat, melt the 1 cup of semi-sweet chocolate chips and 2 tablespoons of butter. Stir until smooth, then mix in 1 1/2 cups powdered sugar, 1/2 cup milk, and 1 teaspoon vanilla extract. Stir until the mixture is smooth and glossy.
Top the Cake: Pour the chocolate mixture evenly over the final layer of graham crackers. Use a spatula to smooth the chocolate topping, ensuring it covers the entire surface of the cake.
Chill: Refrigerate the cake for at least 4 hours, or preferably overnight, to allow the flavors to meld together and the cake to firm up. This will ensure the perfect texture and make the cake easier to slice.