Flour mixture: In a small mixing bowl, stir together flour, cocoa powder, baking powder, and salt. Set aside.
Chocolate mixture: In a small pan on a stovetop, heat the chocolate and butter on very low heat until completely melted. If you aren't able to control the heat of your stovetop well, I'd recommend using a double boiler to prevent the chocolate from seizing.
Whip eggs: Meanwhile, in a large mixing bowl, add the eggs, granulated sugar, brown sugar, peppermint extract, and vanilla extract. Use an electric hand mixer to beat the mixture for at least 5 minutes on medium speed until it becomes pale in colour and doubled in volume.
Combine: Add the melted chocolate mixture into the egg mixture and beat on low speed until combined. Add flour and beat again on low speed until just combined.
Rest batter: Let the batter rest at room temperature for 10 minutes to allow it to firm up.
Prep: Meanwhile, preheat the oven to 350°F. Line a baking sheet with parchment paper and set aside.
Scoop dough: Use a 3 or 4-tablespoon cookie scoop to scoop the cookie dough and release them onto your lined baking sheet, leaving about 2" in between each cookie to account for spreading.
Bake: Bake cookies for 12-14 minutes or until the surface of the cookies is cracked and puffy. Immediately sprinkle crushed candy canes on top of each cookie to let the heat help them stick.
Cool: Let the cookies cool on the baking sheet for about 10-15 minutes before transferring them to a wire rack to cool completely.