Make the cookies: Sift flour, baking powder, and 1/2 teaspoon salt into a bowl. Beat butter and sugar with a mixer on medium speed until pale and fluffy, about 3 minutes. Beat in eggs and vanilla. Reduce speed to low. Gradually mix in flour mixture. Divide dough in half. Flatten each half into a disk, and wrap in plastic wrap. Refrigerate until firm, at least 1 hour.
Preheat oven to 325 degrees, with racks in upper and lower thirds of oven. Let dough stand at room temperature just until soft enough to roll, about 10 minutes. Roll out each disk on a lightly floured surface to a 1/4-inch thickness, adding more flour as needed to keep dough from sticking. Refrigerate until firm, about 30 minutes. Cut out cookies using a 3 1/2-inch round cutter, transferring to parchment-lined baking sheets as you work. Roll out scraps, and repeat once. Freeze cookies until very firm, about 15 minutes.
Bake cookies, switching positions of sheets and rotating sheets halfway through, until edges are golden, 17 to 19 minutes. Let cookies cool completely on sheets on wire racks.
Decorate the cookies: Transfer icing to a pastry bag fitted with a plain round tip. Frost cookies, leaving a border if desired. Let stand overnight to dry.
Mix together luster dust and lemon extract. Place stencil on 1 cookie, and paint with luster dust by dabbing with a small food-safe paintbrush. Repeat with remaining cookies, adding more extract as needed to keep luster loose. (You may need to make another stencil if paper gets soggy.) Let dry completely.
Dough can be refrigerated overnight. Store cookies at room temperature for up to 3 days.