Cream butter, sugar and vanilla until fluffy. Sift flour and salt together; add to creamed mixture, mixing well to make a soft dough. Stir in walnuts. Break off pieces of dough the size of a walnut and shape into balls. Place on ungreased cookie sheet.
Bake in preheated 375 degree oven for 12 to 15 minutes. Remove from cookie sheet with spatula or pancake turner; cool slightly so they won't crumble when handled, then roll in powdered sugar. Yield: 4 dozen.
Notes
To double recipe, double all the ingredients except the salt; leave salt at 1/2 tsp.