In a mixer, cream butter and sugar together until light and fluffy.
Add vanilla and egg, beating well after each addition.
Add flour, baking powder and salt to the dough mixture and mix well.
Shape dough into a disk and wrap with plastic wrap. Chill for at least an hour.
Bake at 375° for 5-8 minutes. I baked mine for 7 minutes. Watch them carefully and take out before the edges brown.