Preheat your oven to 180 C. Line a baking sheet with parchment paper.
In a mixing bowl, add the sugar and egg and mix until creamy using an electric mixer. Add the peanut butter and mix together well.
Form 1 inch balls of dough, a small ice cream scoop would be ideal, or just use two spoons. Place on the parchment paper, goal is 12 balls.
Slightly flatten each ball with the back of a fork, then again at a 90 degree angle to make the crisscross pattern.
Bake for 12 minutes, remove and let cool for 1-2 minutes on the sheet.
Make the filling by adding the butter and peanut butter to a mixing bowl and beat with a electric mixer until smooth, slowly add in the powdered sugar and beat until smooth. Mix in the milk 1 tablespoon at a time to achieve the desired consistency.
Spread a tablespoon of filling on the bottom side of a cookie, top with another cookie, bottom side on the filling. Repeat for the remaining cookies, serve.