Sugar Cookie Cutouts

Sift flour, baking powder, and salt into a bowl.

Put butter and sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until pale and fluffy. Mix in eggs and vanilla. Reduce speed to low. Gradually mix in flour mixture. Divide dough in half; flatten each half into a disk. Wrap each in plastic. Refrigerate until firm, at least 1 hour or overnight.

Preheat oven to 325 degrees with racks in upper and lower thirds. Let one disk of dough stand at room temperature just until soft enough to roll, about 10 minutes. Roll out dough between two pieces of plastic wrap to 1/4 inch thick. Remove top layer of plastic wrap. Cut out cookies with a 4-inch one-piece-shaped cookie cutter. To make an ornament, cut out a hole from the center of the neck about 1/4-inch from the edge using a straw. Transfer cookie dough on plastic wrap to a baking sheet. Transfer baking sheet to freezer, freeze until very firm, about 15 minutes. Remove baking sheet from freezer and transfer shapes to baking sheets lined with nonstick baking mats. Roll out scraps, and repeat. Repeat with remaining disk of dough.

Bake, switching positions of sheets and rotating halfway through, until edges turn golden, 15 to 18 minutes. Let cool on sheets on wire racks.