Whisk the dry ingredients. In a large bowl, whisk together the gluten-free flour, unsweetened dark dutch processed cocoa powder, baking soda, baking powder, espresso powder, and salt. Set the bowl aside.
Cream the butter and sugars. In a large mixing bowl or stand mixer, beat together the melted butter, brown sugar, and white sugar.
Add the egg, vanilla extract, and peppermint extract. Continue to mix until light and fluffy.
Combine the wet and dry ingredients. At low speed, add the dry ingredients to the wet ingredients until just together. Do not over-mix!
Fold in the chips. Add the Andes mint chips and dark chocolate chips to the dough and gently fold to incorporate. Cover the bowl with foil and refrigerate for 2 hours.
Prepare the baking sheets. Preheat oven to 350 degrees F. Line two large baking sheets with parchment paper and set aside.
Scoop and roll the dough. Remove the cookie dough from the refrigerator. If the dough chills over 2 hours and is stiff, let the dough come to room temperature for 15 minutes, then proceed to bake. Use a 1-ounce cookie scoop to scoop the cookie dough into 35-gram balls. Roll the dough with clean palms, and place each ball of dough 2 inches apart on the prepared sheets.
Bake. Place one tray at a time in the oven and bake for 8-9 minutes, or until the edges are just set and the centers have puffed up but are still gooey.
Transfer to a wire rack to cool. If desired, you can use a large circular cookie cutter or circular glass to coax the cookies into perfect circles once removing them from the oven. Let the cookies rest on the baking sheet for 3-4 minutes, then transfer to a wire cooling rack for 1 hour before storing