Step 1 In the bowl of a stand mixer, or in a large bowl using an electric mixer, cream together the butter and sugar. Beat in the egg until combined.
Step 2 Stir in the vanilla, then the baking powder. Slowly stir in the flour until combined. Wrap the dough tightly in plastic wrap and refrigerate until well-chilled, at least 2 hours.
Step 3Heat the oven to 425 degrees. Roll out the dough on a lightly floured surface about one-eighth inch thick. Cut the dough into desired shapes. Place the cookies approximately 1 inch apart on an ungreased baking sheet.
Step 4Bake the cookies in the center of the oven until set, about 5 to 7 minutes (they should not color and may only be faintly golden around the edges). Remove and cool the cookies on a rack. Frost the cookies (below) when cooled, or cover tightly and freeze until ready to frost, up to 2 months; thaw before frosting.