In a medium bowl, cream butter and vanilla until smooth. Combine the 6 tablespoons confectioners' sugar and flour; stir into the butter mixture until just blended. Mix in the chopped walnuts. Roll dough into 1 inch balls, and place them 2 inches apart on an ungreased cookie sheet.
Bake for 12 minutes in the preheated oven. When cool, roll in remaining confectioners' sugar. I also like to roll mine in the sugar a second time.