Preheat oven to 350F and grease an 8" x 8" square brownie pan and line with parchment if you want life to be easier.
In a stand mixer fitted with the paddle attachment cream butter and sugar until smooth. Next, add eggs one at a time, then vanilla and peppermint extracts.
Sift in cocoa powder and mix until completely smooth, then add flour and salt and mix until just combined, don't over mix.
Pour into your greased and lined brownie pan and spread evenly with a spatula.
Bake for 18-20 min. You don't want to over bake, you want them to still be a bit gooey when you pull them out. When they're done, let them cool in the pan for 10 min before you remove and cool the rest of the way on a rack.
While the brownies are baking, make the frosting. Cream the butter until smooth, about 1 min. Add the confectioners' sugar and mix for another two minutes, then add the vanilla. Next sift the cocoa powder in and mix until completely combined, add milk of your choice 1 tbsp. at a time until frosting is smooth but still relatively thick.
Once brownies are cooled, frost and spread crushed candy canes over top. Put in the fridge for an hour until the frosting sets before you cut them. Once set, cut them up into squares. Brownies can be kept at room temperature for 2 days, but they are better in the fridge and can be kept there for up to 1 week.
Notes
Brownies can be kept (without frosting) in the freezer for up to 3 months.