Heat the oven to 350°F and line two baking sheets with parchment. Beat butter and brown sugar until creamy, then beat in egg and vanilla.
Whisk flour, cocoa, baking soda and salt and mix into the butter until a soft dough forms. Divide into 24 balls and place 2 inches apart.
Bake one sheet at a time for 9 to 10 minutes, until the edges are set and the centers are still soft.
Immediately place one unwrapped mint chocolate on each hot cookie. Wait 1 minute, then spread the softened candy over the top with a small knife, leaving uneven chocolate-mint swirls.
Let the cookies stand on the sheets for 10 minutes, then transfer to racks and cool until the chocolate topping is firm.