Preheat the oven to 375°F/190°C and prepare a 9x13 baking dish with nonstick cooking spray.
In a large mixing bowl, combine all finely ground Nutter Butter cookies (minus 1 cup) with the melted butter. Mix well using a fork until the mixture feels and looks like wet sand.
Pour the crumb mixture into the bottom of a 9x13 baking dish, packing firmly and flat using the palms of your hands. Bake for 10-12 minutes or until the crust has hardened and is golden brown. When done, remove it from the oven and allow it to come to room temperature before proceeding.
In a large mixing bowl, beat together the powdered sugar and cream cheese using an electric hand or stand mixture. Beat until smooth. Fold in 1 tub of whipped topping and mix until smooth.
Add cream cheese mixture to the Nutter Butter crust and spread evenly and flat using a rubber spatula.
In a clean large mixing bowl, combine vanilla pudding mix and milk. Beat until the pudding package has completely dissolved and the mixture slightly thickens.
Add in 1 tub of whipped topping, peanut butter, the remaining finely ground Nutter Butter crumbs, caramel sauce, and sea salt. Blend until all ingredients are smooth.
Add mixture to the dish and spread evenly across. Top with the remaining tub of whipped topping before covering the dish and placing it inside the refrigerator to chill overnight.
When ready to serve, garnish the dish with the remaining Nutter Butter cookies, broken into larger crumbs as well as a caramel sauce drizzle.