In a large bowl, beat the cream cheese, butter and confectioners' sugar until smooth. In a large bowl, whisk milk and pudding mixes for 2 minutes; let stand for 2 minutes or until soft-set. Gradually stir into cream cheese mixture. Fold in whipped topping.
Spread 1-1/3 cups of crushed cookies into an ungreased 13-in. x 9-in. dish. Layer with half of the pudding mixture and half of the remaining cookies. Repeat layers. Refrigerate for at least 1 hour before serving. Serve with shaved white chocolate if desired. Yield: 20 servings.