Place 33 Oreo cookies in a food processor and pulse until they are fine crumbs. Remove and set aside a handful of the crumbs for sprinkling on top later; leave the rest in the processor bowl.
With the food processor running, slowly pour in 1/4 cup melted unsalted butter and pulse until the crumbs are evenly moistened.
Press the buttered cookie crumbs evenly into the bottom of a 9×13-inch glass baking dish using clean hands or an offset spatula. Refrigerate the crust while you make the next layers.
In a large chilled bowl, combine 16 oz cold heavy whipping cream, 1/2 cup powdered sugar, and 2 teaspoons vanilla extract. Beat with a stand mixer or hand mixer until soft peaks form.
Divide the whipped cream into two equal portions (about 1 cup each). Set one 1-cup portion aside for the cream cheese layer and reserve the other 1-cup portion for the final topping.
In a separate bowl, beat 16 oz cream cheese (room temperature) with 1/4 cup powdered sugar until smooth and free of lumps.
Gently fold the reserved 1 cup of whipped cream into the cream cheese mixture until combined and smooth.
Spread the cream cheese/whipped cream mixture evenly over the chilled Oreo crust. Return the dish to the refrigerator while you prepare the pudding layer.
In a medium bowl, whisk together the 3.4 oz instant vanilla pudding mix and the 3.9 oz instant chocolate pudding mix with 4 cups cold milk for about 2 minutes, or until the mixture begins to thicken.
Spread the combined pudding evenly over the cream cheese layer. Cover and refrigerate for at least 10 minutes to allow the pudding to set.
Remove the dish from the refrigerator and spread the remaining 1 cup of whipped cream evenly over the pudding layer.
Sprinkle the reserved handful of Oreo crumbs (Oreo crumbles) over the top as a garnish. Chill the assembled lasagna in the refrigerator for another 20 minutes before serving.