Sift flour, cocoa powder, baking soda, baking powder, and salt into a bowl.
Using a stand mixer fitted with the paddle attachment, beat butter, sugar, and espresso powder on medium-high speed until combined and smooth, scraping down sides as needed, about 1 minute.
Reduce speed to medium-low, add yolks and peppermint extract; beat to combine.
Add flour mixture in increments, briefly mixing after each addition.
Divide dough in half, shape into disks, wrap each tightly in plastic wrap, and refrigerate until firm, 1 hour or up to 2 days.
Adjust oven rack to middle position; heat oven to 350°F (177ºC). Line 2 baking sheets with parchment paper. Working with 1 disk at a time, roll dough to ¼-inch thick on a large sheet of parchment paper.
Using a 2¼-inch or 2½-inch cutter, cut dough into shapes; space shapes 1 inch apart on prepared sheets.
Bake one sheet at a time until edges of cookies are dry to the touch, and barely yield in the center, 13–15 minutes; rotating halfway through. Transfer sheets to wire racks; let cookies cool completely on sheets.
Repeat cutting and baking with remaining dough dish. Gently reroll scarps until all dough is used.
Add chocolate to a microwave-safe bowl and microwave in 30 second increments until completely melted and smooth. Drizzle cookies with white chocolate and sprinkle with crushed peppermint candies. Let set then transfer to an airtight container with tight fitting lid.