Preheat oven to 350°F.
Finely crush 40 of the wafers; place in medium bowl.
Add butter and sugar; mix until well blended.
Press firmly onto bottom of 13x9-inch baking pan.
Bake 8 min. or until lightly browned; set aside.
Pour 1-1/4 cups of the milk into medium bowl. Add dry chocolate pudding mix. Beat with wire whisk 2 min. or until well blended.
Spread chocolate pudding mixture over the crust.
Top with remaining 24 wafers.
Pour remaining 2 cups milk into large bowl. Add dry white chocolate pudding mixes. Beat with wire whisk 2 min. or until well blended. Gently stir in whipped topping.
Spread over wafer layer in pan. Refrigerate at least 3 hours or until set.
Preheat broiler just before serving. Top dessert evenly with marshmallows. Broil 1 min. or until marshmallows are puffed and lightly browned.
Sprinkle with shaved chocolate, cut into squares and serve immediately.