Beat the softened butter, 1/2 cup powdered sugar, and the vanilla together in a large bowl until very fluffy.
In a separate bowl, whisk the flour and salt together.
Stir the flour/salt mixture and the nuts into the butter mixture until the dough holds together.
Shape the dough into 1-inch balls and place about 1/2 inch apart on an ungreased cookie sheet.
Bake 7-9 minutes. *They won't change shape at all, so it's a bit hard to tell when they're done. However, they shouldn't be brown at all - it's better to take them out early than have them be overdone.
Remove them from the oven and allow them to rest on the cookie sheet for a couple minutes.
After a few minutes, while the cookies are still warm, roll them in powdered sugar then place them on a cooling rack.
After the cookies are cool, roll in powdered sugar one more time.
Notes:
Make Ahead: These are best served warm or on the day baked. You can easily make up the dough ahead of time and store in the fridge until time to bake. You can also freeze the baked cookies and pull out an hour or two before serving.