• In the bowl of a stand mixer, add the butter and sugar and cream together on medium speed until smooth, ~3 minutes. While the mixer is going, add the flour, cocoa powder, and salt to a small bowl and whisk well to combine, then set aside.
• Once the butter and sugar are smooth, add the egg white and beat to combine, scraping down the sides if necessary. Next add the vanilla and the peppermint extract and beat to combine. It likely won't look like it's mixing well, almost like it's curdled, but don't worry this is ok! Just mix until it's consistent throughout and there are no obvious dry spots or clumps.
• Mixing on low, slowly add the dry ingredients 1/3 at a time, scraping down the sides in between each addition. Stop mixing just when the dough is finally smooth throughout, it will be quite a sticky dough. Lay out two sheets of parchment paper, and divide the dough evenly between the two, placing the dough in the middle of the sheets. Place two more sheets on top of the dough, and using a rolling pin, roll the dough out to 1/4" thickness throughout. Without the parchment paper, the dough would be just too sticky to roll it easily.
• Once both halves of the dough are rolled out, move them, still in their parchment sandwiches, to a baking sheet. Feel free to stack them on top of each other, that's fine. Place the baking sheet in the freezer for 45 minutes. While chilling, preheat the oven to 350°F.
• Line two baking sheets with parchment paper, and set aside. Remove the dough from the freezer, and carefully peel off the top pieces of parchment paper. Using a 2" cookie cutter, cut out cookies in the dough and place on the lined baking sheets, about 1" apart from each other. Ball up the leftover dough and re-roll it out to 1/4" to get more cookies out of the dough. You may need to rechill the dough, as it can quickly become too sticky to work with.
• Bake the cookies for 15-18 minutes, until they feel firm to the touch. Be careful about over-baking though, as it can be difficult to see burning on chocolate cookies. Let the cookies cool for 5 minutes in the pan, and then move to a wire rack to cool completely.

Chocolate Coating

• When the cookies have cooled and are ready to coat, add the chopped chocolate to a medium heatproof bowl, along with the vegetable oil. Microwave for 30 seconds, and stir, and then microwave in 15 second increments, stirring in between each until the chocolate has completely melted. You want it to be completely liquid, so as it's not too thick of a coating over your cookies.
• Once melted, add the peppermint extract and stir to combine. Using a fork, dip the cookies one at a time into the chocolate, making sure they're fully coated, and letting excess drip back into the bowl before gently placing on a lined baking sheet (I just put them back on the sheets that they baked on). Once all the cookies are coated, refrigerate the cookies for at least 10 minutes to set. This chocolate isn't tempered, so I find they're best served chilled as that way the chocolate doesn't immediately start melting in your hand. Also chilled thin mints are always better!
• Enjoy!