Cream together butter, and sugar beat until light and fluffy. Add in egg, baking powder, salt, and vanilla combine well. Stir in flour until well blended and smooth. Refrigerate dough for 45 minutes. Divide dough in half, and put one half back in the refrigerator.
Roll out remaining dough on either wax paper, or a floured board. Roll out until dough is an even 1/4 inch thick. Cut out cookies with cookie cutters, and carefully transfer to a cookie sheet, spacing them 1 inch apart. Bake for 6 to 9 minutes on the top rack in a 350 degree oven. When you remove the cookies let them stand on a cookie sheet briefly to firm up. Cool on racks.