In a large mixing bowl combine the butter and cream cheese. Blend until combined. Add the brown and granulated sugars and beat until lightened and fluffy. Scrape down the sides and bottom of the bowl and blend again. Add the egg and vanilla and beat on medium until well blended.
In a medium mixing bowl whisk together the flour, cocoa powder, baking soda and salt. Add half the flour to the butter and sugar mixture. Mix on low until blended then add the remaining flour. Continue to mix until combined. Cover the cookie dough with plastic wrap and refrigerate until firm, for 1 hour. Cookie dough can be refrigerated overnight if desired.
When ready to bake, preheat oven to 350°F degrees. Line two baking sheets with parchment paper; set aside.
Scoop 1 tablespoon of cookie dough and roll into a 1-inch ball. Place 2 inches apart on the prepared baking sheets. Bake until the cookies are just set, 7 to 9 minutes. The cookies should be puffy in the middle and just set around the edges.
Remove from the oven and immediately top each hot cookie with 1 unwrapped Andes chocolate mint. Allow the chocolate to soften, about 1 to 2 minutes. Using an off-set spatula, knife or the back of a spoon, spread the softened chocolate over the top of the cookie. Transfer to a wire rack and cool completely.
Cookies can be stored in an airtight container at room temperature for 1 week.