Arrange a single, even layer of Nutter Butter cookies across the bottom of a 9x13-inch baking dish.

In a large bowl, beat the softened cream cheese and powdered sugar with an electric mixer until completely smooth and lump-free.

Fold 1 1/2 cups of the thawed whipped topping into the cream cheese mixture using a spatula until evenly incorporated and lightened.

Spoon dollops of the cream cheese mixture over the cookie layer, then spread gently so the cookies are fully covered with an even layer.

In a separate bowl, whisk the chocolate pudding mix with the milk and beat until the mixture becomes thick and smooth, about 3–5 minutes.

Spread the prepared chocolate pudding evenly over the cream cheese layer to form the next layer of the lasagna.

Top the pudding with the remaining whipped topping and smooth it into an even finish over the surface.

Place the leftover Nutter Butter cookies in a sealable bag and crush them; sprinkle the cookie crumbs uniformly over the whipped topping.

Warm the peanut butter in a microwave-safe bowl until pourable, transfer to a plastic bag, snip off a corner, and drizzle the melted peanut butter across the top. Add optional toppings such as chocolate or peanut butter chips if desired.

Refrigerate the assembled dessert for at least 45 minutes to set, then cut into 12 pieces. Keep chilled until serving.