Cookie Dough:

In a large mixing bowl or the bowl of a stand mixer, whip butter on high speed until smooth and creamy, about 30 seconds.

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

Add egg and milk and mix until well combined. Mixture may look slightly separated.

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

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

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

Cover bowl with plastic wrap and refrigerate until very firm, at least 2 hours, or overnight.

With a 1 1/2-inch cookie scoop, divide the dough into equal portions. You should have about 22-24 total.

Arrange on a parchment-lined plate and freeze for 15 minutes, or refrigerate for 30 minutes.

Meanwhile, preheat oven to 350° F (175° C). Line a half sheet rimmed baking tray with parchment or a silicone baking mat.

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

Bake in preheated oven for 13-15 minutes, or until puffy and set. Do not overbake.

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 with remaining cookie dough.

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, or add the chocolate to the top of a double boiler.

Melt dark chocolate, stirring occasionally, until completely melted.

Meanwhile, warm 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 until smooth.

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 thick and 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 stepped palette knife, spread ganache over each cookie.

Garnish with miniature candy canes, or additional crushed candy cane pieces.

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

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.