Preheat oven to 350 degrees F. Line baking sheets with parchment paper and set aside.
Beat butter sugars, and milk in the bowl of a stand mixer fitted with the paddle attachment until light and fluffy, about 8-10 minutes.
In a medium size bowl, sift flour, cocoa, and baking soda. Once the butter/sugar is light and fluffy, add dry ingredients and mix until a dough forms. Stir in chocolate pieces. Wrap dough with plastic wrap and refrigerate 30 minutes.
Roll cookie dough into 1 tbsp sized balls and arrange on baking sheets (no more than 8 at a time). Using the bottom of a measure cup or drinking glass, gently flatten the dough slightly and bake 10-12 minutes.
Remove cookies from oven and let cool on a cooling rack. Repeat with remaining dough.
Once all of the cookies are baked and completely cooled, make the filling. Beat powdered sugar, peppermint extract, and cream with an electric mixer until combined. The filling should be firm enough to hold its shape. If your filling is too runny, add more powdered sugar 1 tablespoon at a time until desired consistency. Alternatively, if your filling is too firm, add more heavy cream 1 teaspoon at a time.
Spread frosting onto the flat side of a cookie and sandwich with another. Repeat with remaining cookies.