On medium speed, cream the butter and 1/2 cup powdered sugar until light and fluffy. Add the vanilla and flour; continue beating until well mixed. Stir in nuts. Cover and chill dough for one hour. Shape dough into 1" balls and place on ungreased cookie sheets. Bake (350 degrees) for 15 minutes (watch carefully so they don't get too brown). Let stand on cookie sheet for 2 - 3 minutes. Roll in remaining powdered sugar. Cool completely and roll in powdered sugar again. These are delightful!!!!
P.S. You must use butter in these cookies; do not substitute margarine or you will not get the same flavor.