Place the Oreo cookies in a food processor and pulse until they are crumbly.
Slowly pour the melted butter into the cookie crumbs while pulsing until evenly combined.
Reserve a handful of the crumbs for garnish, then press the remaining buttered crumbs firmly into the bottom of a 9×13-inch glass baking dish to form the crust.
Refrigerate the crust while you prepare the fillings.
Make the whipped cream: in a chilled bowl combine the 16 oz cold heavy whipping cream, 1/2 cup powdered sugar, and 2 teaspoons vanilla extract; beat with a stand or hand mixer until soft peaks form. Set aside.
In a separate bowl, beat the softened 16 oz cream cheese with 1/4 cup powdered sugar until smooth.
Gently fold half of the prepared whipped cream (about 1 cup) into the cream cheese mixture until combined and spread this mixture evenly over the chilled Oreo crust.
Return the dish to the refrigerator while you make the pudding layer.
In a bowl, whisk together the 3.4 oz vanilla and 3.9 oz chocolate instant pudding mixes with 4 cups cold milk for about 2 minutes, until smooth and slightly thickened.
Spread the combined pudding mixture evenly over the cream cheese layer.
Cover and chill for at least 10 minutes to set the pudding layer.
Spread the remaining whipped cream over the pudding layer.
Sprinkle the reserved Oreo crumbs on top, chill for another 20 minutes, and serve chilled.