Grease a 9x13-inch glass baking dish and set aside.
Arrange a single layer of peanut butter sandwich cookies to fully cover the bottom of the baking dish (about 22 cookies); reserve the remaining cookies for the topping.
In a mixing 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.
Use a whisk or hand mixer to fold 1 cup creamy peanut butter and the additional 1 cup whipped topping into the thickened pudding until smooth.
Spread the peanut butter pudding layer 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 the top with ½ cup peanut butter chips and the chopped reserved cookies, then drizzle with the ½ cup melted creamy peanut butter.
Chill the assembled lasagna in the refrigerator for 30 minutes (or in the freezer for 15 minutes) before serving.