Beat butter and sugar on medium speed until pale and fluffy, 2 to 3 minutes.

Add egg and vanilla, beat to combine. Whisk flour, baking powder, and salt, then gradually add to mixer on low until a dough forms.

Pat dough into a disc, wrap in plastic, and refrigerate at least 1 hour.

Preheat oven to 350°F (180°C). Roll dough ¼ inch thick, cut shapes, and place 2 inches apart on parchment-lined sheets.

Bake 8 to 10 minutes until edges are barely set. Cool on sheet 5 minutes, then transfer to a rack.

Frost cooled cookies with glaze or royal icing and decorate while wet. Let icing set fully before stacking.