For the cookies:
1½ cups all-purpose flour
2/3 cup Dutch-process cocoa powder
Pinch of salt
12 tbsp. (6 oz.) unsalted butter, at room temperature
1½ cups confectioners’ sugar
2 large eggs
1 tsp. peppermint extract
½ tsp. vanilla extract
6 oz. bittersweet chocolate, finely chopped
10 oz. good quality white chocolate, finely chopped
Crushed candy canes or peppermint candies
To make the cookies, combine the flour, cocoa powder and salt in a small bowl; whisk to blend and set aside. In the bowl of an electric mixer, combine the butter and sugar. Beat on medium-high speed until light and fluffy, 2-3 minutes. Blend in the egg, peppermint extract, and vanilla. With the mixer on low speed, add the dry ingredients and mix just until incorporated and no streaks remain. Form the dough into a disc, wrap tightly with plastic wrap and refrigerate until firm, 1-2 hours.
Preheat the oven to 325? F. Line a baking sheet with parchment paper or a silicone baking mat. On a lightly floured work surface, roll the dough out to about ¼-inch thickness. Cut out 3-inch rounds with a cookie cutter and place cut outs on the prepared baking sheet. Bake 10-12 minutes, just until set. Let cool on the baking sheet about 5 minutes, then transfer to a wire rack to cool completely.
Line baking sheets with wax or parchment paper. Place the bittersweet chocolate in a heatproof bowl set over a few inches of simmering water. Heat, stirring occasionally, until the chocolate is melted and smooth. One a time, dip the bottom side of each cookie into the chocolate. Use an offset spatula to scrape of the excess, leaving only a very thin layer of chocolate on the bottom of the cookie. Place on the prepared baking sheets. Transfer to the refrigerator to chill until the chocolate has set, about 15 minutes.
Repeat the melting process with the white chocolate in the double boiler set up. Use an offset spatula to spread a layer of white chocolate on top of each cookie and sprinkle immediately with crushed candy cane pieces before the chocolate sets. Transfer to the refrigerator to chill again just until set, about 15 minutes more. Store in an airtight container.