In a food processor mix together sugar, brown sugar, flour, cocoa, baking soda and salt. Add the butter a few pieces at a time, with the motor running. Pulse to incorporate. Add the egg and vanilla. Pulse until the dough starts to form. Turn the dough onto a clean surface. Form into a log/rope that is about 1 1/2 inches in diameter. Wrap in plastic wrap, and let chill in the refrigerator for 60 minutes.

Preheat oven to 350° F.

Remove dough from the fridge and remove plastic wrap. Using a sharp knife, slice dough about 1/4 inch thick. Place dough on a lined baking sheet about 2 inches apart. Bake for 12-15 minutes until set and cookies look dry. Remove from the oven and cool completely.

Meanwhile, prepare the filling. Cream together butter and brown sugar. Mix in the peanut butter, vanilla and milk. Stir in flour and salt until well combined.

Once the cookies are completely cooled, use a cookie scoop to place a round ball of cookie dough in the center of the cookie. Place another cookie on top, and gently press down. Repeat until all of the cookies are gone. You may have a little extra filling, it depends on how thick you make them.