1 Whisk together flour, cocoa powder, baking powder, and salt in a bowl.
2 Beat butter and sugar in a seperate bowl with an electric mixer until pale and fluffy about 2 minutes, then beat in yolk and vanilla. On low speed, beat in flour mixture just until a dough forms.
3 Divide the dough in half, flatten each piece into a disc and then chill them, wrapped in plastic wrap, until firm, for 2 to 3 hours.
4 Preheat oven to 350°F 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 (? inch thick). Cut out as many stars as possible, reserving and chilling scraps, then quickly transfer cookies to the baking sheet, arranging them ½ inch apart. (If dough becomes too soft, return it to the freezer until it is firm. )
5 Bake until firm and slightly puffed, about 10 minutes. Cool cookies on baking sheet for 5 minutes, then transfer to a rack to cool completely. (Cookies will crisp as they cool. ) Make more cookies with remaining dough and scraps, rerolling scraps only once.
6 To make the icing, in an electric mixer fitted with the whisk attachment, beat egg white and cream of tartar until foamy. Sift in half the sugar and beat until smooth, about 1 to 2 minutes. With mixer running, gradually add remaining sugar and beat on high speed until icing is smooth and thick. Icing should be thick, but not too thick to be pressed through a pastry bag. Adjust consistency with more confectioners’ sugar or water.
7 Transfer icing to a pastry bag with a small round tip. Pipe icing onto cookies and add decorations of your choice, before icing hardens.