In a small bowl, combine flour, cocoa powder, baking powder, and salt; set aside.
Melt chocolate and butter together in a small saucepan over very low heat or use a double boiler until smooth.
In a large bowl, beat eggs, granulated sugar, brown sugar, peppermint extract, and vanilla extract with an electric mixer on medium speed for at least 5 minutes until pale and doubled in volume.
Slowly add the melted chocolate mixture to the egg mixture and beat on low speed until combined.
Add the flour mixture and beat on low speed until just incorporated.
Let the batter rest at room temperature for 10 minutes to firm up.
Preheat oven to 350°F and line a baking sheet with parchment paper.
Using a 4-tablespoon cookie scoop, place dough balls on the baking sheet spaced 2 inches apart.
Bake for 12-14 minutes until cookies are cracked and puffy on top.
Immediately sprinkle crushed candy canes on top to adhere while cookies are hot.
Allow cookies to cool on the baking sheet for 10-15 minutes before transferring to a wire rack to cool completely.