20 tablespoons unsalted butter (2 1/2 sticks), softened to cool room temperature (about 65 degrees)
1/2 cup cocoa powder (about 2 ounces)
1 teaspoon espresso powder
1 cup sugar (7 ounces)
1/4 teaspoon table salt
2 large egg yolks
2 teaspoons mint-flavored extract
2 1/4 cups unbleached all-purpose flour (11 1/4 ounces)
Glaze
4 ounces bittersweet chocolate
4 tablespoons unsalted butter
2 tablespoons corn syrup
1 teaspoon vanilla extract
1 cup white chocolate chips , melted
1. Adjust oven rack to middle position; heat oven to 375 degrees. Melt 4 tablespoons butter in medium saucepan over medium heat (or in medium microwave-safe bowl, on medium power for about 30 seconds). Add cocoa powder and espresso powder; stir until mixture forms smooth paste. Set aside to cool, 15 to 20 minutes.
2. In standing mixer fitted with paddle attachment, mix remaining 16 tablespoons butter, sugar, salt, and cooled cocoa mixture on high speed until well combined and fluffy, about 1 minute, scraping sides of mixing bowl once or twice with rubber spatula. Add yolks and mint extract and mix on medium speed until thoroughly combined, about 30 seconds. Scrape sides of bowl. With mixer running on low, add flour in three additions, waiting until each addition is incorporated before adding the next and scraping bowl after each addition. Continue to mix until dough forms cohesive ball, about 5 seconds. Turn dough onto counter; divide into three 4-inch disks. Wrap each disk in plastic wrap and refrigerate until the dough is firm yet malleable, 45 to 60 minutes. (Alternatively, shape dough into log 2 inches in diameter and about 12 inches long; use parchment paper or plastic wrap to roll into neat cylinder. Chill until very firm and cold, at least 1 hour.)
3. Roll out 1 dough disk between 2 large sheets parchment paper to even thickness of 3/16 inch. (If dough becomes soft and sticky, slide rolled dough on parchment onto baking sheet and rechill until firm, about 10 minutes.) Peel parchment from one side of dough and cut into desired shapes using cookie cutter(s); using thin metal spatula, place shapes on parchment-lined baking sheet, spacing them about 1-inch apart. Gather dough scraps and chill. (For log-shaped dough, simply slice cookies 1/4 inch thick and place on parchment-lined baking sheets.)
4. Bake until cookies show slight resistance to touch, 10 to 12 minutes, rotating baking sheet halfway through baking time; if cookies begin to darken on edges, they are overbaked. Repeat with second and third portions of rolled dough. Cool for 5 minutes, then, using spatula, transfer cookies to wire rack; allow to cool completely. Repeat steps 3 and 4 with remaining dough disks and scraps, rerolling scraps just once.
5. For Glaze: In bowl set over pot of simmering water, melt chocolate with butter and whisk until smooth. Remove bowl from pot, add corn syrup and vanilla, and mix until smooth and shiny. Use back of spoon to spread scant 1 teaspoon glaze almost to edge of each cookie. (If necessary, reheat to increase fluidity of glaze.) Allow glazed cookies to dry at least 20 minutes. Drizzle melted white chocolate chips over glazed cookes. Let dry at least 20 minutes before serving.