Grease a 9x13-inch glass baking dish and set aside.
Arrange a single layer of peanut butter sandwich cookies to completely cover the bottom of the prepared dish (about 22 cookies); reserve the remaining cookies for the topping.
In a bowl, beat the softened cream cheese with the powdered sugar and 1 cup whipped topping until smooth and well combined.
Spread the cream cheese mixture evenly over the cookie base, then place the dish in the freezer to chill for 15 minutes.
Whisk the instant vanilla pudding mix with 1½ cups whole milk until it begins to thicken according to the package directions.
Using a whisk or hand mixer, fold 1 cup creamy peanut butter and an additional 1 cup whipped topping into the slightly thickened pudding until smooth and uniform.
Spread the peanut butter pudding mixture over the chilled cream cheese layer, then return the dish to the freezer for another 15 minutes to firm.
Gently spread the remaining 2 cups whipped topping over the chilled peanut butter layer.
Sprinkle the top with ½ cup peanut butter chips and the chopped reserved whole peanut butter cookies, then drizzle the ½ cup melted peanut butter over the surface.
Chill the assembled dessert in the refrigerator for 30 minutes (or in the freezer for 15 minutes) before serving.