Crush the sandwich cookies into fine crumbs using a food processor or by sealing them in a zippered bag and pounding with a rolling pin. Set aside roughly half a cup of the crushed cookies for topping. Combine the remainder with melted butter until well moistened. Firmly press the mixture into the base of a 9x13-inch baking dish to form an even crust. Place the pan in the refrigerator to set while preparing the next layer.

In a separate bowl, whip the softened cream cheese until smooth and creamy. Add in the powdered sugar and mix until thoroughly blended. Gently fold in one cup of the whipped topping until incorporated. Spread this mixture in an even layer over the chilled cookie crust.

In a clean mixing bowl, vigorously whisk together the pudding mixes and cold milk for about 2 minutes until it thickens slightly. Let it stand for 5 minutes to fully set, then spread the pudding evenly over the cream cheese layer.

Cover the pudding with the remaining whipped topping, smoothing it into an even layer. Sprinkle the top with the reserved cookie crumbs or garnish with chocolate shavings as desired. Cover the dish and refrigerate for a minimum of 4 hours, or overnight for best results.

Slice into squares and serve cold.