In a large mixing bowl beat butter and sugar. Add in egg, milk, and vanilla extract, blending thoroughly.
In a separate bowl, stir together flour, cocoa, baking soda, and salt. Add to butter mixture, incorporating well. Refrigerate dough for about 1 hour or until firm enough to handle. (Dough will still be a little soft).
Preheat oven to 350°F. Lightly grease a cookie sheet, line with parchment paper, or use a silicone baking mat. Remove wrappers from peppermint patties.
Roll dough into 1 ¼ inch balls. For each cookie flatten the ball slightly and gently press one peppermint pattie into the dough. Mold dough around the pattie so that it is completely covered. Place on prepared cookie sheet..
Bake 12 to 14 minutes or until the cookie is set. Cool slightly, about 3 minutes on the baking sheet before removing from cookie sheet to wire rack. Cool completely.