Preheat your oven to 350°F (or 175°C). Butter an 8X8 baking pan, and line it with parchment paper, leaving some overhang on two sides.
In a large glass bowl, add in the butter and dark chocolate, and microwave at 30-second intervals until they are fully melted.
Whisk in the cocoa powder until just combined and the mixture looks smooth. Wait for about 5 minutes for it to cool down.
Stir in the sugar until just combined, stir in the eggs, one at a time, until just combined, and stir in the peppermint extract until just combined. Now, add in the flour and gently stir until well combined, and you can see any streaks of flour.
Pour the batter into the already lined pan, and allow it to spread evenly. Tap on the countertop to disperse any air bubbles.
Bake in your preheated oven for about 40 minutes, or until a toothpick comes out through the center clean. Allow to cool for another 20 minutes, lift out of the pan, and place on a rack to cool completely.
Add the chocolate chips into a small glass bowl, and microwave at 30-second intervals until fully melted. Drizzle the melted chocolate over the brownies, and sprinkle some crushed peppermint candy canes over it.
Allow to set, before slicing into squares, and serving.