Preheat the oven to 350°F (180°C). Line a baking sheet with parchment paper. Set aside.
Add softened butter and white and brown sugar to your stand mixer and cream them together until smooth.
Add peppermint extract and egg and mix in.
Add the all purpose flour, cocoa powder, baking soda and salt and mix it with a spoon into a thick cookie dough (don't use your electric mixer for this part).
Add the milk and mix in.
Break off pieces of the dough and roll it into balls. Place the balls evenly on your parchment lined baking tray. Aim to get 20 balls from your batch.
Press down on them with a fork to flatten.
Bake for 10 minutes. Allow to cool completely before doing the topping.
Break up the white chocolate and add to a microwave safe bowl with the coconut oil. Microwave in 30-second intervals, bringing it out to stir every 30-seconds until melted.
Stir in peppermint extract. If the chocolate is a bit too thick to easily work with then stir in another teaspoon of coconut oil.
Use a teaspoon to spoon the white chocolate over the cookies so that they are covered from the top.
Immediately sprinkle on the crushed candy canes. Place the whole tray in the fridge for the chocolate to set.