Cookie Dough:

In a large mixing bowl or the bowl of a stand mixer, whip butter until light and fluffy.

Add granulated sugar and brown sugar and mix on medium-high speed until well combined.

Add egg and milk and mix until well combined.

In a separate bowl, whisk flour, cocoa powder, baking soda, and kosher salt.

Add dry ingredients to butter mixture, and mix on low speed until just combined.

With a rubber spatula or wooden spoon, stir in the white chocolate chips and crushed candy canes.

Cover bowl with plastic wrap and transfer to refrigerator to chill, at least 2 hours or overnight.

Once dough has chilled, use a 1 1/2-inch cookie scoop to divide the dough into equal portions.

Place cookie dough balls on a parchment-lined plate and freeze for 15 minutes, or chill in the refrigerator for 30 minutes.

Meanwhile, preheat oven to 350° F / 175° C. Line a rimmed half-sheet baking tray with parchment.

Transfer half of the cookie dough balls on the prepared tray, allowing space for the cookies to spread. Return the remaining balls of dough to the refrigerator until ready to use.

Bake in preheated oven for 13-15 minutes.

If desired, use a large round metal cutter to gently reshape the cookies into perfect circles.

Cool on tray for 10 minutes, then transfer to a wire rack to cool completely. Repeat process with the remaining cookie dough.

While cookies cool, prepare the ganache.

For the Ganache:

Add chopped dark chocolate to a large metal bowl.

Sit bowl over a pot of simmering water to create a bain-marie, or hot water bath. (Alternately, you can use a double boiler.)

Gently melt dark chocolate, stirring occasionally, until completely melted.

Meanwhile, warm whipping cream in a small saucepan over low heat, stirring occasionally. (Do not boil.)

Remove chocolate from heat. Slowly pour warm cream mixture into the melted chocolate and whisk to combine.

Whisk in the peppermint oil.

Allow ganache to sit at room temperature for 10-15 minutes, then whisk vigorously for 2-3 minutes, or until creamy. You will feel the mixture thicken, and it will lose some of its glossy sheen, looking less like melted chocolate and more like chocolate frosting.

To Assemble:

With a metal teaspoon or a small palette knife, apply a spoonful of ganache to each cookie, then spread it evenly over the top.

Garnish each cookie with a miniature candy cane, or additional crushed candy cane pieces.

Allow cookies to sit uncovered for 30 minutes, or until ganache is set.

Chocolate peppermint cookies are best enjoyed on the day they are made. Store leftovers in an airtight container at room temperature for up to 3 days. Chocolate peppermint cookies can also be frozen in an airtight container between sheets of parchment.