Preheat oven to 350 degrees.
Cream butter and sugar; beat in egg and vanilla. Sift flour and baking powder together, stir into mixture. Refrigerate about 1 hour, or until dough is firm enough to roll. On a floured surface, roll to 1 /8-inch thickness and cut with cookie cutters. Sprinkle the tops with granulated sugar. Bake 10-12 minutes at.
Yield: 8 dozen small cookies.