Beat together butter and confectioners' sugar in a medium-size bowl until smooth and creamy. Add vanilla. Beat in flour and nuts. Cover dough with plastic wrap; refrigerate until firm, 1 to 2 hours.
Heat oven to 325 degrees F.
Pinch off pieces of dough in rounded teaspoonfuls. Roll into logs. Taper ends; bend into crescents. Place on an ungreased baking sheet.
Bake in heated 325 degree F. oven 19 to 20 minutes or until lightly browned.
Remove cookies to a wire rack. Sprinkle with a heavy layer of confectioners' sugar. Cool completely. Sprinkle again with confectioners' sugar.
Nutritional Information: (per cookie)
67 Calories; 1 g Protein; 5 g Fat; 6 g Carbohydrate;
1 mg Sodium; 9 mg Cholesterol