Prepare a 9-by-13-inch baking dish. Crush the Oreo cookies into fine crumbs in a food processor. Set aside 3/4 cup of crumbs for the topping.
Stir the remaining crumbs with the melted butter and press them into the bottom of the dish. Put the dish in the freezer for a few minutes while you prepare the next layer.
Beat the softened cream cheese and confectioners' sugar until smooth. Beat in one tub of Cool Whip for about 30 seconds. Do not overbeat.
Place the cream cheese mixture evenly across the crust, then spread it gently so you do not pull up the Oreo base.
In a separate bowl, beat the milk and both packages of instant chocolate pudding mix for about 2 minutes. Spread the pudding evenly over the cream cheese layer.
Spread the second tub of Cool Whip over the pudding and sprinkle with the reserved Oreo crumbs. Chill at least 6 hours before cutting.
Notes
The total time includes at least 6 hours of chilling. Keep refrigerated.