Add pudding mix to a medium bowl with the milk and whisk until just combined.
Add peanut butter to a small bowl and microwave for 20 seconds to soften.
Whisk softened peanut butter into pudding mixture until well combined and place in fridge for 10 minutes.
While pudding sets, place Cool Whip in a medium mixing bowl.
Soften jelly in the microwave for 20 seconds. Stir together jelly and Cool Whip until just combined, being careful not to deflate the Cool Whip by overmixing.
Slice strawberries into thin slices.
Place a single layer of Nutter Butters in the bottom of a 2-quart oval dish. Top with 1/2 of the Cool Whip mixture, followed by half of the pudding mixture and half of the strawberries. Repeat layers, ending with strawberries on top.
If there are any remaining cookies, crush and sprinkle the crumbs over the top of the strawberries.
Let set in fridge for 2 hours to allow the cookies to soften before serving.