Preheat oven to 400°.
Cream together the butter and sugar.
Add the egg and the vanilla, mix until well blended.
In a separate bowl, sift together the flour and baking powder then gradually add to the butter mixture and blend well.
Form the dough into a smooth ball. Roll out the dough on a lightly floured surface to a thickness of ⅛ to ¼ inch.
Cut out with cookie cutters and place on ungreased cookie sheets.
Fill each cookie sheet with cookies of equal size to ensure even baking.
Bake for 6 minutes (a bit longer for thicker cookies), but they shouldn’t brown at all. Remove from cookie sheets and cool on wire racks or waxed paper. Decorate as desired when cool.