Make the Crust: Place the cookies in a food processor blender and process until they are broken down into fine crumbs. Add the melted butter and pulse a few times to ensure that all of the crumbs are evenly moistened. Turn the crumbs out into a 9x13-inch pan and press into an even layer. Refrigerate while the peanut butter layer is prepared.
Make the Peanut Butter Layer: In a large mixing bowl, cream together the cream cheese and peanut butter until smooth and homogenous, about 2 minutes. Reduce the speed to medium-low and gradually add the powdered sugar until it is all incorporated. Increase the speed to medium and beat for 30 seconds. Using a rubber spatula, gently fold in the Cool Whip. Spread in an even layer over the crust and sprinkle with the chopped peanut butter cups. Refrigerate while the pudding layer is prepared.
Make the Pudding Layer: In a large bowl, whisk together the pudding mix and milk for 2 minutes. Let sit for 5 minutes to allow it to set. Use an offset spatula to spread the pudding in an even layer over the cream cheese mixture.
Spread the remaining 8-ounce tub of Cool Whip on top and sprinkle with the rest of the chopped peanut butter cups. Cover and refrigerate for 2 hours before serving.