Stir together the brownie mix, eggs, vegetable oil, water, vanilla, and peppermint extracts to make a smooth batter.
Line pan with parchment paper sprayed with Baker's Release spray into a glass 8x8 inch baking pan for easy removal.
Spread batter into pan.
Top batter with the Andes candy bits (for brownies) (reserve the the other half used in the frosting).
Bake brownies for about 50-55 minutes or until the batter no longer jiggles in the center.
Cool completely.
Mix the powdered sugar and soft butter with the remaining extracts and stir in enough of the milk to make a spreadable frosting; tint frosting with several drops of food coloring as desired.
Stir in 2/3 of the remaining chips into the frosting and spread on the brownies, sprinkling the last of those on top with the crushed candy cane.
Frosting sets (dry enough to handle) in 30-45 minutes.
Slice and serve as desired. Store remainder in an airtight container.