Preheat oven to 350 degrees.
Using a stand mixer fitted with the paddle attachment or a hand mixer beat softened butter and brown sugar on high for 1-2 minutes. Scrape down the bowl once complete.
Add in milk, egg, and melted chocolate. Mix until combined. Scrape down the bowl once complete.
In separate bowl, whisk dry ingredients together (flour, cocoa powder, baking soda, salt).
Add dry ingredients to wet ingredients in 3-4 portions. Mix until combined
Using a wooden spoon, mix in the mint chocolate and white chocolate chips. Reserve ¼ cup of chocolate chips and ¼ of mint chocolate chips to top the cookies right after they come out of the oven.
Grease and line baking sheets with parchment paper or silicone baking mat.
Remove the peppermint frosting from the freezer.
Use a cookie dough scoop a spoon to scoop out a 1-inch dough ball. Then flatten the dough out and place small spoonful of frosting in the center of the dough. Fold the dough over the frosting (ensure it is fully covered by cookie dough) and roll dough into a ball.
Place the dough balls on to baking sheet, leaving at least 1 inch in between each cookie.
Bake for 8-10 minutes or until the cookies just begin to crack.
Remove the cookies from the oven and immediately top with remaining white chocolate chips and mint chocolate chips.
Let cookies cool on baking sheet for 5-10 minutes, then transfer to cooling rack.