Preheat the oven to 350℉. Line baking sheets with parchment paper.

In a large bowl, cream together the softened butter, sugar, and brown sugar for 1 minute using an electric handheld mixer or a stand mixer fitted with the paddle attachment on high speed.

Add the egg, vanilla, and peppermint extract and continue creaming until fluffy. Add the flour and baking soda and mix at low speed just until fully incorporated.

Scoop the cookie dough using a medium-sized cookie dough scoop onto the prepared baking sheets, placing each cookie 2 inches apart to allow room for spreading.

Bake in the preheated oven for 10-12 minutes or until slightly golden around the edges. Let cool fully before topping with the icing.

In a small bowl, whisk together the melted butter, icing sugar, vanilla and peppermint extract, and food coloring, adding the milk until a smooth icing with a consistency that you can drizzle is reached.

Add icing to a ziplock bag (or piping bag) and drizzle or spoon and spread over the cooled cookies. Top with crushed candy canes while the icing is still wet. Enjoy!