Pour 1¾ cups milk into a large bowl. Add dry pudding mix and beat with wire whisk 2 minutes. Gently stir in whipped topping. Layer one-third of the crackers and half of the whipped topping mixture in a 13-by-9-inch pan, breaking crackers as necessary to fit; repeat layers. Top with remaining crackers.
Microwave chocolate and butter in medium microwaveable bowl on high for 1 ½ minutes, stirring after 1 minute. Stir until chocolate is completely melted. Add sugar and remaining ¼ cup milk; stir until well blended. Immediately spread over grahams.
Refrigerate at least 4 hours or overnight. Store any leftovers in refrigerator.