In a bowl, combine the crushed cookies with the melted butter. The mixture should resemble wet sand. If necessary, add more butter or cookie crumbs until it reaches the desired texture.

Press the mixture evenly into a 9x13-inch pan. Refrigerate while you prepare the filling.

Beat the cream cheese, vanilla, and powdered sugar until smooth. Fold in the Cool Whip and spread evenly over the chilled crust.

In a separate bowl, whisk together the instant chocolate pudding mixes and cold milk until the mixture thickens. Let it set for a few minutes, then spread it over the cream cheese layer.

Sprinkle the reserved, crushed Oreo pieces on top of the pudding layer.

Cover the dessert and refrigerate for at least 2 hours until firm. Slice and serve cold.