In a small, microwave-safe bowl, combine butter and chocolate. Microwave for 30 seconds and stir. If necessary, microwave for an additional 15 seconds, stir, and repeat until mixture is smooth. Set aside to cool slightly.
In a medium bowl, whisk together brown sugar, egg, and vanilla. Whisk in chocolate mixture until well-combined.
Add flour, cocoa powder, baking powder, and salt, and stir until just combined. Fold in mints and cookies.
Lay a sheet of cling wrap on the counter, and scrape dough out of the bowl, onto the cling wrap.* Wrap dough and press it out so you have a rough rectangle. Chill dough for 45 minutes, until firm.
Preheat oven to 325°F and line a baking sheet with parchment paper or silicone baking mat.
Unwrap dough and use a dough scraper or knife to cut into six even pieces. Roll the dough into balls and place them on the prepared baking sheet at least 2 inches apart. (For prettier cookies, press a couple extra pieces of Oreo into the top of each cookie before baking.)
Bake for 11 to 13 minutes, until the edges of the cookies are crinkled and centers look set.
Cool cookies on the baking sheet and enjoy! (If desired, place extra Andes pieces on the cookies right after they come out of the oven.)