Cream together butter and powdered sugar until light and fluffy; stir in vanilla.
Whisk together flour and salt; add gradually to butter mixture; stir in chopped nuts.
Chill dough if it seems too soft.
Form dough into 1 1/4" balls and place onto parchment-lined or ungreased baking sheets.
Bake at 400° for 10-12 minutes or just until the cookies start to turn light golden-brown.
Remove from oven and allow to cool slightly; while cookies are still warm (but NOT hot) remove them from baking sheets and roll, a few at a time, in powdered sugar until evenly coated; cool cookies completely on wire racks.
Cookies may (optionally) be rolled in powdered sugar a second time once cooled to room temperature.