Preheat oven to 350, and line a baking sheet with parchment paper.
Combine all ingredients for the cookies in a large bowl and whisk until combined evenly.
Scoop 1 tbsp of the dough and roll into a log with your hands. Place on the prepared baking sheet 2 inches apart. You should have about 24 logs.
Flatten each log with a fork making a crisscross shape, then pinch the middle to make the shape of a peanut.
Bake in the preheated oven for 10 minutes until the edges are firm. Cool on the baking sheet for a few minutes before gently removing to a wire rack to cool completely.
Using a hand mixer or a stand mixer, cream together butter, peanut butter, and powdered sugar. Add milk and mix again until it's a creamy and spreadable consistency. You can add a little bit more milk, if needed.
Add about 2-3 tsp of the filling to the bottom side of one cookie, and then top with another cookie. Repeat with the rest of the cookies. Enjoy!
