In the bowl of a stand mixer or in a large bowl with an electric hand mixer, cream the butter, brown sugar, and white sugar until fluffy and well combined.

Mix in the egg and vanilla extract.

Add in the flour, cocoa powder, baking soda, and salt. Mix until just combined.

Cover and chill the dough in the refrigerator for at least 30 minutes. (Meanwhile, you can use this time to make your peppermint bark.)

When ready to bake, preheat the oven to 350ºF. Line a baking sheet with parchment paper and set aside.

Divide the dough into 6 equal portions, form each portion into a ball, and place them on the lined cookie sheet.

Bake the cookies for 10-12 minutes. Let the cookies cool on the baking sheet for 10 minutes then transfer them to a cooling rack. 

Line a baking sheet with parchment paper and set aside.

In a microwave-safe bowl, melt the chocolate chips in 30-second intervals, stirring after each, until melted and smooth. Spread the melted chocolate out in an even layer on the parchment paper.

In a separate bowl, repeat the process with the white chocolate; melting and spreading it on top of the semisweet chocolate.

Sprinkle with peppermint pieces.

Refrigerate for 30 minutes, or until set. Let sit at room temperature for 15 minutes before breaking into pieces. 

Use a hand-held or stand mixer fixed with a paddle attachment to whip together the butter, confectioners sugar, 3 Tbsp of milk, vanilla extract, and peppermint extract. Add a bit more milk as needed to thin out the frosting to reach your desired consistency.

Transfer the frosting to a piping bag with a round tip or a freezer bag with the tip snipped off. Pipe the buttercream in a swirl on top of the cooled cookies.

Top each cookie with a few pieces of peppermint bark.

Add additional crushed peppermint pieces to the tops of cookies, if desired.