Prepare chocolate pudding according to the box instructions and set in the fridge. You will have extra pudding leftover. Pudding will be thick and creamy in about 15 minutes once chilled.
Add whole cookies to a food processor, and process until crumbs are fine. Mix processed cookies with melted butter and mix to combine. Firmly pat down the cookie layer into a parchment-lined baking dish. Chill for ten minutes before next step.
Add room temperature cream cheese, powdered sugar, vanilla extract, milk, and peanut butter into a large mixing bowl. Using a hand mixer, beat for about one minute until creamy. Fold in 1 cup of whipped topping into the mixture.
Remove dessert pan from the fridge, and layer on the peanut butter layer with a rubber spatula. Smooth over until evenly spread over the cookie layer. Place in the refrigerator for 5 minutes.
Remove pudding from the refrigerator, and the dessert pan and layer on a thick pudding layer. Expect to have about 2 cups of pudding leftover. Place pan in the freezer for 15 minutes before the last cream layer.
Remove dessert pan from the freezer and layer on the 12 ounces of whipped topping with a rubber spatula. Smooth cream over the top of the dessert, and return it to the freezer for 30 minutes before adding the final toppings.
Microwave the peanut butter for 20-30 seconds until creamy. Remove layered dessert from the freezer and add toppings. Sprinkle the peanut butter cups, and morsels evenly over the top of the dessert. Swizzle over the sauces and return dessert to the refrigerator.
Allow dessert to chill for one hour in the freezer to be able to cut nice slices from it. Store any leftovers in the refrigerator.
Using a large, wet knife, and metal spatula to carefully carve and remove slices from the dessert.