Crush 40 wafers; mix with butter and sugar. Press onto bottom of 13x9-inch pan. Bake 8 min. or until lightly browned. Cool.
Beat chocolate pudding mix and 1¼ cups milk with whisk 2 min.; spread over crust. Cover with remaining wafers. Whisk vanilla pudding mixes and remaining milk 2 min. Stir in COOL WHIP. Spread over wafer layer in pan. Refrigerate 3 hours.
Heat broiler. Top dessert with marshmallows; broil 1 min. or until marshmallows are lightly browned. Top with grated chocolate.