1. Make the dough. In a large mixing bowl, combine together the flour, cocoa powder, baking powder, baking soda and salt. In the bowl of a stand mixer fitted with the paddle attachment, or with an electric mixer, cream the butter until light and fluffy, about 1 minute. Add in both sugars and mix for an additional minute, or until well combined. Add the eggs, one at a time, followed by the vanilla and peppermint extract and mix until incorporated. With the mixer running on low, slowly add the dry ingredients and mix until just combined. The dough will be thick. Add the crushed candy cane and chocolate chips. Cover and chill the dough for a least 1 hour.
2. Preheat the oven to 350 F. Line two large baking sheets with parchment paper or a silicone baking mat. Using about 1.5 tablespoons of dough per cookie, scoop the dough onto the prepared baking sheet. I had about 9 cookies per sheet. Bake the cookies for about 10 minutes before removing them from the oven. They should look slightly underbaked. I like to press a few chocolate chips and pieces of candy cane into the tops at this stage. Cool the cookies on the sheet for 5 minutes before removing to a wire rack to completely cool.
3. Once the cookies have cooled completely, melt the white chocolate using a microwave-safe bowl and heating the chocolate in 30 second intervals, stirring each time. Drizzle the white chocolate over the cookies. Allow the chocolate to harden before storing.

Cookies may be stored at room temperature, in an airtight container for 4-5 days, or in the freezer for up to 2 months. Cookie dough can also be stored in the freezer for up to 2 months.