Beat the butter with the sugar. Add the egg and vanilla and beat until you get a uniform mixture. Mix the flour and baking powder and gradually blend them into the mixture. When you're done, you should have a rather sticky dough.

Shape the dough into balls, about 1 inch in diameter. Roll them in sugar and place them on an ungreased cookie sheet, leaving about an inch of space between cookies, so that they don't stick together when they expand.

Bake in preheated oven at 350 degrees F. for 20 minutes. Remove from oven, let them cool for a while, and start eating right away.