In a medium bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and salt. In the bowl of a stand mixer or in a large bowl with an electric mixer, beat together the sugar and butter on medium speed until creamy and well combined, about 1 minute. Reduce the speed to medium-low and add first the egg and then the egg yolk, beating well after each addition. Beat in the vanilla and peppermint extracts. Slowly beat in the flour mixture until just combined. The dough will be super sticky.
Dust the cookie dough, your hands, and a piece of parchment paper with confectioners’ sugar. Shape the dough into a disk on the parchment paper. (If the dough is too sticky to work with, chill it in the fridge for 30 mins) Wrap the disk of cookie dough in plastic wrap and refrigerate until firm, at least 30 minutes. (You can refrigerate the dough up to overnight, though you’ll need to let it warm slightly at room temperature before you’re able to roll it out.)
Preheat the oven to 350°F and adjust the oven racks to the middle and upper third positions. Line 2 baking sheets with parchment paper.
Roll out the dough on the parchment (and covered with the plastic wrap to prevent sticking to the rolling pin)until it’s about 1/8 inch thick. Using a 1 1/2-inch round cutter, cut out cookies from the dough and place them 1/2 inch apart on the prepared baking sheets. Re-roll any scraps and cut out more cookies. Freeze the cutouts for about 15 minutes.
Bake the Thin Mints, switching the baking sheets from top to bottom and front to back halfway through, until dry and crisp and firm around the edges, anywhere from 8 to 15 minutes, depending on thickness. Let the cookies cool slightly on the baking sheets and then transfer them to wire racks to cool completely.
Meanwhile, melt the chocolate chips in a double boiler. Submerge a cookie into the melted chocolate and turn to coat. Shake off any excess and place on parchment paper. Repeat for all of the cookies, re-heating the chocolate when necessary.
Let cookies cool for at least 30 minutes or pop them in the freezer for 15.
Cookies will keep, layered between sheets of parchment paper in an airtight container, for up to 1 week - ha, if you have any last that long!