Beat pudding mix and 1 3/4 c. milk in large bowl with whisk for 2 minutes. Stir in Cool Whip. Layer about 1/3 of the graham cracker squares and 1/2 of the cool whip mixture into a 9x13 pan, breaking graham crackers as necessary to fit. Repeat layers. Top with layer of graham cracker squares.
Microwave chocolate and butter in medium microwavable bowl for 1 1/2 minutes, stirring after 1 minute. Stir until chocolate is completely melted. Add powdered sugar and remaining milk; stir until well blended.