Sift flour, baking powder, and salt together in a bowl and set aside. Beat butter in a bowl with an electric mixer on medium speed. Gradually add sugar and beat until mixture is light and fluffy. Beat in egg and vanilla, then reduce speed and gradually add flour mixture until just combined. Divide dough in half and wrap in plastic wrap. Refrigerate for at least 1 hour.

Preheat oven to 325°. Roll out half of dough 1/8" thick, on a lightly floured surface, cut into desired shapes, arrange 1" apart on buttered nonstick cookie sheets, and decorate as you like. Bake for 5 minutes, rotate baking sheet, and bake until golden, about 5 minutes more. Transfer cookies to a wire rack to cool, then finish decorating as desired.