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 medium bowl, beat the softened cream cheese, 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.
Using a whisk or hand mixer, fold 1 cup creamy peanut butter and 1 cup whipped topping into the pudding until smooth and evenly combined.
Spread the peanut butter pudding layer evenly over the chilled cream cheese layer and return the dish to the freezer for another 15 minutes to set.
Gently spread the remaining 2 cups whipped topping over the peanut butter layer.
Sprinkle peanut butter chips and the chopped reserved cookies over the top, then drizzle the melted ½ cup peanut butter over everything.
Chill the assembled dessert in the refrigerator for 30 minutes or in the freezer for 15 minutes before cutting and serving.
