Crush the chocolate sandwich cookies into fine crumbs using a food processor or by placing them in a sealed plastic bag and crushing them with a rolling pin.
In a mixing bowl, combine the crushed cookies with melted butter. Stir until the mixture is well combined and resembles wet sand.
Press the cookie mixture evenly into the bottom of a 9x9 inch baking dish to form the crust. Place it in the refrigerator to set while you prepare the next layers.
In another mixing bowl, beat the softened cream cheese and powdered sugar together with an electric mixer until smooth and creamy.
Spread the cream cheese mixture over the chilled cookie crust in the baking dish.
In a separate bowl, whisk together the chocolate pudding mix and milk for about 2 minutes until thickened. Pour the pudding over the cream cheese layer, spreading it evenly.
Spread the whipped topping over the pudding layer, smoothing it out to cover the dessert evenly.
Sprinkle chocolate shavings or mini chocolate chips on top for decoration.
Cover the dessert with plastic wrap and refrigerate for at least 2 hours before serving to allow it to set properly.