Use a food processor or blender to crush the Oreos into very fine pieces.
Combine the instant vanilla pudding with the milk. Whisk it well and refrigerate for at least 10 minutes, or until set.
Stir the Oreo crumbs and the Cool whip into the pudding mixture. Then stir in the chocolate pudding.
Let set for at least 15 minutes in the refrigerator, preferably an hour. Even longer is better.
Serve alone like a pudding, in a trifle, as a brownie topper, or combine with buttercream for a cupcake icing.