Add the vanilla pudding mix, peanut butter, and 1 cup of the milk into a large bowl.
Using an electric hand mixer, whip until smooth.
Slowly add two more cups of the milk and whisk until completely smooth.
Fold in 8 ounces of whipped topping until no streaks are left, set aside.
Place nutter butters into the bottom of a 9x13-inch baking dish. Five across in four rows.
Brush the milk generously on each cookie. You really want to soak them.
Add ⅓ of the pudding mixture and spread it out evenly over the cookies.
Add another row of cookies and brush with milk.
Then, add another ⅓ of the pudding mixture and smooth it out.
Repeat 1 more time.
Add a final layer of cookies brushed with milk.
Spread the remaining whipped topping over the cookies.
Cover with plastic wrap and place in the fridge overnight.
If you want to add peanut butter garnish, microwave a small amount of peanut butter in a microwaveable dish and cook in 15 second intervals, stirring in between until smooth and melted.
Drizzle the peanut butter over the cake and add more cookies if desired. Slice and serve.