Start by preheating your refrigerator to chill the dessert after preparation.
In a mixing bowl, crush the 36 Oreo cookies into fine crumbs using a fork or rolling pin. Combine the crushed cookies with melted butter. Stir until the mixture is well combined.
Press the cookie mixture evenly into the bottom of a 9x13 inch baking dish to form the crust. Set aside.
In a separate bowl, beat the softened cream cheese and powdered sugar together with an electric mixer until smooth. Gently fold in 1 cup of whipped topping until well combined.
Spread the cream cheese mixture over the cookie crust in the baking dish.
In another mixing bowl, whisk together the chocolate pudding mixes and milk until thickened, about 2 minutes. Pour the pudding over the cream cheese layer, spreading it evenly.
Top the chocolate pudding layer with the remaining 1 cup of whipped topping, smoothing it out with a spatula.
Crumble a few extra Oreo cookies on top for garnish, if desired. You can also add chocolate shavings or mini chocolate chips for an extra touch.
Cover the baking dish with plastic wrap and refrigerate for at least 2 hours to allow the dessert to set.
Once chilled, cut into squares and serve cold.