Prepare Cookie Dough:
In a large bowl, beat the butter, granulated sugar, and brown sugar together with a hand-held or stand mixer on medium-high speed for 3 minutes, until light and fluffy. Add the egg and vanilla extract, beating until well combined and scraping down the sides of the bowl as needed.
Mix Dry Ingredients:
In a separate bowl, whisk the flour, cocoa powder, baking soda, and salt until combined.
Combine Wet and Dry Ingredients:
Turn the mixer to low and gradually add the dry ingredients to the wet ingredients to avoid flour spillage. Add the chopped Andes mints and mix using a rubber spatula until evenly incorporated.
Chill the Dough:
Cover the dough tightly with plastic wrap and chill for at least 3 hours, or up to 3 days. This step is crucial for thicker cookies.
Preheat Oven:
Preheat the oven to 350°F and line two large baking sheets with parchment paper. Let the dough sit at room temperature for 30 minutes if it has chilled for longer than a day.
Shape and Bake:
Scoop out the dough using a large cookie scoop and arrange the dough balls on the prepared baking sheet 2-3 inches apart. Bake for 10-12 minutes, or until the edges are set and the tops look slightly soft.
Top with Andes Mint:
Immediately after baking, press a whole Andes mint into the top center of each warm cookie. Let them melt, then use a toothpick to swirl the mint around. If the cookies lose their circular shape slightly in the oven, use a wide-mouthed cup to swirl around the outside to create a perfect shape.