Preheat the oven to 350°F. Line a 9 x 9-inch or 8 x 8-inch pan with parchment paper.
In a stand mixer or a large bowl using a hand mixer, mix together the cooled melted butter, sugar, and cocoa powder. Beat in the eggs one at a time. Stir in the coffee, vanilla extract, and peppermint extract. Stir in flour and salt just until all ingredients are combined.
Pour the batter into the prepared pan. Top with an even layer of the Andes mints. Bake at 350°F for 35 to 40 minutes, when a toothpick inserted into the center of the brownies comes out clean. Allow to cool at room temperature.
Make the Frosting
While the brownies are cooling, make the frosting. Clean out the stand mixer to reuse, or use a large bowl with hand mixer. To the stand mixer bowl or your large bowl, beat the butter until it's light and fluffy, about 2 minutes. Mix in the powdered sugar, one cup at a time, until incorporated. Pour in the milk and peppermint extract. If using food coloring, add in the drops of food coloring now. Gently fold in the chocolate chips.
Using a spatula, spread the frosting over the brownies in an even layer. Sprinkle chopped extra Andes mint candies and then slice into 9 squares or 12 rectangles.
Notes
Andes mint chocolates: One standard size box of Andes mint chocolate candies is usually enough for the batter and for the decoration. Feel free to get two boxes and add more mint chocolate candies as decoration if you wish. Use a maximum of 28 mint chocolate candies to top the brownie batter as more will affect the way the brownies bake; I find 24 to be just about right. Storage: These brownies will keep in an airtight container at room temperature for up to 5 days, although they are best eaten within 1-2 days. You can also freeze brownies and frosting in separate containers.