Place 1 layer of graham crackers in the bottom of a 9x13 casserole dish. Whisk together pudding mix and milk until thick and creamy, about 3 minutes.
Gently fold in defrosted from frozen whipped topping until completely mixed in. Spoon half of the pudding mixture over the graham crackers and spread into an even layer. Cover the pudding with a layer of graham crackers and top with remaining pudding in another layer.
Top with additional graham crackers to for the final layer. Place chocolate chips in a medium bowl, heat milk in a microwave until warm, about 30 seconds.
Pour milk over chocolate chips and allow to rest until the chocolate has melted. Stir until well incorporated.
Using a mixer, beat in the melted butter. When well mixed, add the powdered sugar and whip until completely incorporated. Continue to mix for an additional 2 to 3 minutes or until the frosting is smooth and fluffy.
Spread the topping over the final layer of graham crackers. Cover the dessert and refrigerate overnight before serving to allow the crackers to soften.