Whisk together first 3 ingredients in a bowl until blended and smooth. Fold in 1 1/2 cups whipped topping.
Spoon 1 Tbsp. crumbs into each of 6 (4-oz.) glasses, and top with 1/3 cup pudding mixture. Repeat layers with remaining crumbs and pudding mixture. Top each parfait evenly with remaining whipped topping and grated chocolate. Cover and chill at least 1 hour.