In the bowl of a stand mixer fitted with the paddle attachment, beat butter at medium speed until creamy, about 1 minute. Add confectioners’ sugar, vanilla, and salt; beat until smooth, about 1 minute. With mixer on low speed, gradually add flour and cocoa, beating until combined.

Turn out dough onto a sheet of parchment paper, and shape into a 6-inch square. Wrap in parchment, and refrigerate for at least 1 hour or up to overnight. (If refrigerating overnight, let dough stand at room temperature for 30 minutes before rolling.)

Line baking sheets with parchment paper.

On a lightly floured surface, roll dough to ⅜-inch thickness. Using a 2½- to 3½-inch holiday cutter dipped in flour, cut dough, rerolling scraps and cutting to use all dough. Place 2 inches apart on prepared pans. Refrigerate for 20 minutes.

Preheat oven to 325°F (170°C).

Bake until tops and edges are set, 10 to 15 minutes, rotating pans after 8 minutes of baking. Let cool on pans for 10 minutes. Remove from pans, and let cool completely on wire racks.

Dip tops of cooled cookies in Espresso Glaze, letting excess drip off, and garnish with turbinado sugar, if desired. Store in an airtight container for up to 3 days.