In a large-size bowl using an electric handheld mixer on medium speed, beat together the softened butter and eggs until combined.

Sift the cocoa powder and cake mix together using a sieve into the wet ingredients and mix on low speed until the dry ingredients are well combined - the dough will be soft. Cover the dough and refrigerate for 30 minutes.

Preheat the oven to 350℉. Line 2 baking sheets with parchment paper. When done chilling, roll the dough into balls, using about 1 ½ tablespoons of dough per cookie. Place on the prepared pans leaving spreading room between each cookie.

Bake the pans of cookies in the preheated oven for 10-12 minutes or until the tops start to crack. Let cool on the pan for 5 minutes before transferring to a wire rack to finish cooling completely before sandwiching with the frosting. Bake the remaining cookies.

In a medium bowl using an electric handheld mixer on medium speed, whip the softened butter until fluffy. Add the powdered sugar, peppermint extract, and vanilla and beat on low speed until well combined. Add milk if the texture is too thick. Add food coloring, 1 drop at a time, until your desired color is achieved. Pipe or spread with a knife, about 1 tablespoon of frosting per cookie, onto half of the cooled cookies. Sandwich together with the plain cookies. Enjoy!