1. Sift flour, salt, and baking powder together into a bowl. With an electric mixer, beat butter and granulated sugar on medium-high speed until pale and fluffy, about 3 minutes. Mix in egg and vanilla. Reduce speed to low; gradually mix in flour mixture. Wrap dough in plastic wrap. Chill 1 hour.

2. Preheat oven to 325 degrees. Let dough stand at room temperature 10 minutes. Generously flour a large sheet of parchment. Roll out dough on parchment to a scant 1/4-inch thickness, running an offset spatula under dough and dusting with flour as necessary to prevent sticking. Transfer dough on parchment to freezer, and chill 15 minutes.

3. Using a 2- to 3-inch X- or O-shaped cookie cutter, quickly cut out shapes from dough. (If dough begins to soften, return to freezer for 3 to 5 minutes.) Reroll scraps once and cut out more shapes.

4. Transfer shapes to parchment-lined baking sheets, spacing them 2 inches apart. Freeze 15 minutes. Sprinkle shapes with sanding sugar. Bake until edges are just golden, 15 to 18 minutes. Let cool completely on sheets on wire racks.