Step 1: Preheat and Prepare. Preheat your oven to 350°F (175°C). Grease an 8×8 inch square baking pan or line it with parchment paper, leaving an overhang on the sides for easy removal later.
Step 2: Mix the Brownie Batter. In a large bowl, whisk together the melted butter and granulated sugar. Add the eggs one at a time, followed by the vanilla and peppermint extracts. Sift in the cocoa powder, flour, salt, and baking powder. Fold the dry ingredients into the wet ingredients until just combined. Do not overmix.
Step 3: Bake the Brownies. Pour the batter into the prepared baking pan and spread it evenly. Bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Allow the brownies to cool completely in the pan.
Step 4: Prepare the Fudge Frosting. In a medium bowl, beat the softened butter and cocoa powder together until smooth. Gradually add the powdered sugar, milk, and peppermint extract. Beat on medium speed until the frosting is light and fluffy. If it is too thick, add more milk one teaspoon at a time.
Step 5: Frost and Decorate. Once the brownies are entirely cool, spread the fudge frosting evenly over the top using a spatula. Immediately sprinkle the crushed candy canes over the frosting, pressing them down lightly so they stick.
Step 6: Slice and Serve. Lift the brownies out of the pan using the parchment paper. Use a sharp knife to cut them into 16 squares. Wipe the knife between cuts for the cleanest edges.