For the Dough:
2 cups all-purpose flour
½ cup Dutch-process cocoa powder
½ teaspoon baking powder
½ teaspoon salt
2 sticks (8 ounces) unsalted butter, softened
¾ cup granulated sugar
1 large egg yolk
1 teaspoon pure vanilla extract
For the Filling:
½ stick (2 ounces) unsalted butter, at room temperature
¼ cup vegetable shortening
2 cups sifted confectioners' sugar
2 teaspoons vanilla extract
Garnish: Decorative sugar (optional)
1. Whisk together the flour, cocoa powder, baking powder and salt.
2. Beat butter and sugar with an electric mixer until pale and fluffy, then beat in yolk and vanilla. At low speed, mix in flour mixture in 3 batches just until a dough forms. Divide dough in half and form each piece into a 6-inch square, then chill, wrapped in plastic wrap, until firm, 2 to 3 hours.
3. Preheat oven to 350 degrees F. Grease two baking sheets or line with parchment paper or a silicone baking mat.
4. Roll out 1 piece of dough between sheets of parchment paper into a 14x10-inch rectangle (1/8-inch thick). Slide dough in parchment onto a tray and freeze until dough is firm, about 10 minutes. Repeat with remaining dough.
5. Cut out as many rounds as possible from first chilled square with a 2-inch fluted or round cutter, reserving and chilling scraps, then quickly transfer cookies to a buttered baking sheet, arranging them ½ inch apart. (If dough becomes too soft, return to freezer until firm.)
6. Sprinkle half of cookies with decorative sugar (if using), then bake cookies until baked through and slightly puffed, 10 to 12 minutes. Cool on sheet on rack for 5 minutes, then transfer to rack to cool completely (cookies will crisp as they cool).
7. Make more cookies with remaining dough and scraps (re-roll only once).
8. To make the filling, beat the butter and shortening together at medium speed until combined and smooth. Reduce the speed to low and gradually beat in the sugar and vanilla. Increase the speed to high and beat for 2 to 3 minutes until the filling is light and fluffy.
9. To assemble the cookies, pipe a heaping teaspoon of filling onto the flat side of the plain cookies. Top with the sugared cookies to make sandwiches. Store in an airtight container at room temperature.