Preheat the oven to 350°F. Line a 9x13 baking pan with parchment paper. Leave enough parchment overhang on two sides to lift the chilled brownies from the pan.
Prepare brownies as directed on the box. Pour into the prepared pan. Bake according to the package directions, beginning to check for doneness around 20 minutes. Insert a toothpick into the center and look for moist crumbs rather than wet batter. Let the brownies cool completely before adding the peppermint layer.
While the brownies are cooling, beat powdered sugar, ½ cup butter (softened), cream, and peppermint in a large bowl. Spread evenly over the cooled brownies.
Refrigerate for 30 minutes.
In a small pot, melt mini chocolate chips and ½ cup butter over low heat, stirring constantly. Spread over chilled brownies.
If serving soon, add crushed candy canes while the chocolate is still soft. Chill again for 30 - 60 minutes to help set up quicker, if desired. For neat slices, chill the brownies until the chocolate topping is fully set. Use a sharp knife warmed under hot water, then wipe it dry between cuts.