Cut your butter in pieces, place them into a stainless steel pan (or a light-colored one) over medium heat.
Stir and always keep an eye on it. Once melted, the butter will begin to foam. Keep stirring until it turns golden brown.
The butter will be ready when you'll see browned specks at the bottom of the pan. Pour it into a bowl to cool down at room temperature.
Make cookie dough:
Using a stand mixer with flat hook (or by hand, using a whisk), beat butter and sugars at medium high speed for 2 minutes until you get a pale mixture.
Add the egg, vanilla extract and peppermint extract and let incorporate for a few seconds.
Now add flour, baking soda, salt and cocoa powder and stir with a spatula just until incorporated.
Now add the chopped dark chocolate chips, 1 crushed candy cane (the other one will be used on top) and stir with the spatula again. Do not overmix. Alternatively you can use 2 candy canes inside the dough.
Let chill into the fridge for about 30 minutes.
Preheat the oven at 345°F (175°C).
Using an ice cream scoop to form the cookies and arrange them well spaced on 2 lined baking trays. I place 5 on a tray, 5 on another.
Bake for 11-13 minutes. While you bake one batch, place the other into the fridge.
IMPORTANT: they will be ready when their edge looks crisp and the center looks soft. DON'T overbake, we want chewy cookies right?;)
A few minutes after taking them out of the oven, place a chocolate chip on top of the cookie. As mentioned in the other recipe, these chips are heavy and for this recipe I've used a total of 125 gr (which is about 1 cup).
If your cookies are not round once baked: while they are still warm use a round food ring to make them "rotate" and smooth out the edges. (this is a tip I've learned from Mike @mikebakesnyc)