Preheat the oven to 350°F and line two cookie sheets with parchment paper
In a stand mixer fitted with the paddle attachment, beat the butter and the two sugars together on medium-high speed until light and fluffy (around 2 minutes). Then, add the egg and vanilla and continue beating on medium speed until the mixture is smooth and creamy (around one more minute).
Sift the flour, cocoa powder, baking soda, and salt together. Then, add these to the bowl of your mixer. Beat everything together on low speed, until the flour is just combined. Do not overwork the dough. Lastly, add the crushed candy canes and use a flexible spatula to fold them into the dough.
Wrap the dough and place it into the fridge to chill for at least half an hour or overnight.
Scoop 1.5" balls of dough and drop them onto the cookie sheets. Leave 1.5-2 inches of space between each cookie. Bake for 11-12 minutes, or until the cookies are puffed up and edges are set. Once you take them out of the oven, let the cookies rest for 5 minutes on the baking sheet before transferring them to wire racks to cool completely.
For the drizzle, place the white chocolate chips into a small microwave safe bowl. Heat them in the microwave in 20 second spurts, stirring between each until the chocolate is fully melted. Be careful to not burn the chocolate. If needed, add ½ tsp of oil into the chocolate to help make it smooth and easier to drizzle. Spoon the chocolate over the cookies, let it set, and enjoy!