Chocolate Sandwich Cookies with Peppermint Buttercream Filling

1. 1
   Place the egg yolk and vanilla in a small bowl and stir to combine; set aside.
2. 2
   Combine the measured flour, sugar, cocoa powder, and salt in a food processor fitted with a blade attachment and pulse a few times to aerate and break up any lumps. Add the butter and pulse until the mixture looks like sand, about 25 (1-second) pulses. Add the reserved yolk mixture and pulse just until the dough forms into a ball, about 30 (1-second) pulses.
3. 3
   Turn the dough out onto a lightly floured work surface and divide it into 2 equal portions. Using your hands and flouring them as needed, roll each portion into a log about 1 1/2 inches in diameter. Wrap each log in plastic wrap and refrigerate until just firm but still pliable, about 1 hour. (The logs will flatten slightly while chilling. If you have a paper towel tube available, cut it in half lengthwise and nestle the cookie dough in there; this will help the dough keep its cylindrical shape while it chills.) Reshape the logs so they are perfectly round and refrigerate until firm, about 1 hour more.
4. 4
   Heat the oven to 350°F and arrange the racks to divide the oven into thirds. Line 2 baking sheets with parchment paper; set aside.
5. 5
   Remove a dough log from the refrigerator, remove the plastic wrap, and slice the dough into 1/8-inch coins. Place the cookies 1/2 inch apart on the prepared baking sheets (about 20 cookies per sheet).
6. 6
   Place both sheets in the oven and bake for 9 minutes. Rotate the sheets front to back and top to bottom and continue baking until the edges of the cookies are firm but the tops are still soft, about 7 to 8 minutes more.
7. 7
   Place the baking sheets on wire racks and let cool for 5 minutes. Using a flat spatula, transfer the cookies to the wire racks to cool completely. Let the baking sheets cool completely and repeat with the remaining dough (you can reuse the parchments).

For the filling:

1. 1
   Place the mint candies in a resealable plastic bag. Using a meat mallet, crush them into tiny pieces, but don’t totally pulverize them into a powder. (Alternatively, you can use a frying pan to crush the candies.) You should have about 1/3 cup; set aside.
2. 2
   Combine the powdered sugar and butter in the bowl of a stand mixer fitted with a paddle attachment and mix on low speed until crumbly, about 2 minutes. Gradually increase the speed to medium and beat until smooth, about 2 minutes more. Add the vanilla and beat until smooth, about 1 minute. Stop the mixer and scrape down the paddle and the sides of the bowl with a rubber spatula.
3. 3
   Increase the speed to high, add the crushed candies, and beat until just combined, about 10 seconds. Place the filling in a large resealable plastic bag, push to one bottom corner, and cut a 1/2-inch opening in that corner.
4. 4
   Flip half of the cooled cookies onto their tops, and pipe the filling (about a heaping teaspoon) onto each cookie bottom. Close with the cookie tops and gently press to flatten until the filling reaches the edges. Store in an airtight container at room temperature for up to 3 days.