1. Into medium-sized bowl, measure flour, butter or margarine, vanilla, salt, and 1/2 cup confectioners' sugar; knead ingredients until blended. Stir in chopped walnuts. Shape dough into a ball; wrap with plastic wrap and refrigerate 1 hour or until firm enough to handle.
2. Preheat oven to 400°F. Shape dough into 1-inch balls. Place balls, about 1 inch apart, on ungreased cookie sheet.
3. Bake cookies 10 to 12 minutes until set but not brown. With pancake turner, remove cook ies to wire racks to cool. Repeat with remaining dough. Onto sheet of waxed paper, measure 1/2 cup confectioners' sugar.
4. When cookies are cold, roll them in confectioners' sugar to coat completely. Store cookies in tightly covered container.