Make the crust. Place the peanut butter sandwich cookies in a food processor and pulse until fine crumbs form. You can also crush them in a zip-top bag using a rolling pin. Combine the crumbs with the melted butter and stir until the mixture looks like wet sand. Press the mixture firmly into the bottom of a lightly greased or parchment-lined 9x13-inch baking dish. Chill the crust while you prepare the next layer.

Prepare the chocolate pudding layer. In a medium bowl, whisk the instant chocolate pudding mix with the cold milk for about 2 minutes, or until the mixture thickens. Spread the pudding evenly over the chilled crust, using an offset spatula to reach the corners. Return the dish to the refrigerator so the pudding can set while you make the peanut butter cream layer.

Create the peanut butter cream layer. In a large mixing bowl, beat the softened cream cheese, powdered sugar, and creamy peanut butter until smooth and lump-free. Gently fold in the thawed whipped topping. Use a light hand here because folding too aggressively will deflate the mixture. Spread the peanut butter cream over the chilled pudding layer.

Add the topping. Sprinkle the milk chocolate chips and peanut butter chips evenly over the top. Press them in just slightly so they adhere to the creamy layer.

Chill and serve. Cover the dish with plastic wrap or a lid and refrigerate for at least 4 hours. Overnight chilling is even better because it allows the layers to firm up completely. When ready to serve, cut into 12 bars and keep chilled until serving time.