Use a mixer to beat softened butter with granulated and brown sugar until fluffy (about 2–3 minutes). Add an egg and vanilla, then mix on high speed until smooth, scraping the bowl as needed.
In a separate bowl, whisk together flour, cocoa powder, baking soda, and salt. Gradually add to the wet mixture on low speed, then stir in milk to form a sticky dough.
Cover and refrigerate for at least 2 hours (up to 3 days). Chilling makes the dough easier to handle and ensures even baking.
Preheat the oven to 350°F (177°C) and line baking sheets. Scoop dough into 25g balls, roll in sugar for a sparkly finish, and space 2–3 inches apart on the sheets.
Bake for 10–12 minutes. If cookies don’t spread by minute 9, tap the tray on the counter a few times, then return to the oven to finish.
While still warm, press an unwrapped Andes mint onto each cookie. Let it melt for 5 minutes, then swirl with a knife or spatula for a glossy finish.
Cool completely on a rack and enjoy. Once set, cookies can be stacked and stored at room temperature in an airtight container for up to a week.