In a medium bowl, whisk together flour, cocoa powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer, cream the butter and sugars on until light and fluffy (about 2-3mins). Reduce speed and add the eggs and peppermint extract. Mix until well combined.
Add flour mixture and mix until just combined.
Chill dough for at least 1 hour or overnight.
Preheat oven to 350°F and line baking sheets with parchment paper or silicone mats.
Using a medium cookie scoop (1 1/2 tablespoons), portion dough into balls and place on the baking sheet, about 2" apart.
Bake for 8-10 minutes, or until the middle is set.
Cool on the pan for 5 minutes then transfer to a wire rack to cool completely.
Melt the chocolate chips according to the package instructions with 1 teaspoon canola oil. Place the melted white chocolate in a ziptop bag, snip a tiny hole in one corner and drizzle over the top of the cookies. Immediately sprinkle the crushed candy canes over the white chocolate
Allow to set.