In a medium bowl, whisk together the pudding mix with the milk for 2 minutes. Let sit for 5 minutes.
Line an 8x8-inch square baking dish with Nutter Butter cookies.
Drizzle with one-third of the melted peanut butter.
Spread half of the pudding over top of the cookies and peanut butter. Top with half of the Cool Whip, then sprinkle with half of the chopped peanut butter cups.
Repeat the layers of Nutter Butter cookies, another third of the melted peanut butter, remaining half of the pudding and remaining half of the Cool Whip.
Garnish the top by drizzling the remaining melted peanut butter and additional chopped peanut butter cups and crushed Nutter Butter cookies.
Cover with plastic wrap and refrigerate overnight (this is essential so that the cookies soften). The dessert can be refrigerated for up to 4 days.