This requires a 2 or 3-inch fluted star or snowflake cookie cutter.

Whisk together flour, cocoa powder, baking powder, and salt. Beat butter and sugar with an electric mixer until pale and fluffy about 2 minutes, then beat in yolk and vanilla. On low speed, mix in flour mixture just until a dough forms. Divide dough in half, flatten each piece into a disc and then chill them, wrapped in plastic wrap, until firm, 2 to 3 hours.

Preheat oven to 350 degrees with racks in top and bottom thirds. Line 2 baking sheets with parchment paper.  Roll out 1 piece of dough between sheets of parchment paper into a 14-by 10-inch rectangle (1/8 inch thick). Cut out as many stars as possible, reserving and chilling scraps, then quickly transfer cookies to the baking sheet, arranging them 1/2 inch apart. (If dough becomes too soft, return to freezer until firm.)

Bake it until firm and slightly puffed, about 10 minutes. Cool on baking sheet 5 minutes, then transfer them to a rack to cool completely (The cookies will crisp as they cool.) Make more cookies with remaining dough and scraps, rerolling scraps only once. The finished cookies can be decorated with icing.