1 cup all-purpose flour, plus more for surface
1/2 cup unsweetened Dutch-process cocoa powder
1/2 teaspoon baking soda
1/2 teaspoon baking powder
1/2 teaspoon salt
2 1/2 ounces (5 tablespoons) unsalted butter, softened
3/4 cup sugar
1 large egg
1 large egg yolk
3/4 teaspoon pure peppermint extract
8 large candy canes or 30 peppermint candies, crushed
2 pounds white chocolate, coarsely chopped

Directions

1. Preheat oven to 325 degrees. Sift flour, cocoa powder, baking soda, baking powder, and salt into a bowl.
2. Beat butter and sugar with a mixer on medium-high speed for 1 minute. Reduce speed to medium-low, and add egg, then yolk, beating well after each addition. Beat in peppermint extract.
3. Slowly add flour mixture, and beat until just incorporated. Shape dough into 2 disks, wrap each in plastic, and refrigerate until firm, at least 1 hour (or up to 2 days).
4. Roll out 1 disk of dough on a lightly floured surface to 1/8-inch thickness. Freeze until firm, about 15 minutes.
5. Using a 2-inch round cutter, cut out circles, and place 1 inch apart on parchment-lined baking sheets. Roll and cut scraps once. Freeze cookies until firm, about 15 minutes. Repeat with remaining disk. Alternately, form dough into tablespoon-sized balls with your hands. Freeze the balls for about 15 minutes, then press flat with a glass.
6. Bake until cookies are dry to the touch, about 12 minutes. Transfer parchment, with cookies, to wire racks, and let cool. (Undecorated cookies will keep, covered, for up to 3 days.)
7. Sift crushed candy, and separate larger pieces from dust, reserving both.
8. Melt chocolate in a heatproof bowl set over a pot of gently simmering water. Remove from heat. Dunk cookies into melted chocolate. Using a fork, turn to coat, let excess drip off, and gently scrape bottom against edge of bowl. Place on parchment-lined baking sheets, and sprinkle 1/4 teaspoon of either candy pieces or dust on top. Repeat, sprinkling half the cookies with pieces and the rest with dust. Refrigerate until set, up to 3 hours. Decorated cookies are best served the same day.

Makes about 3 dozen.