Preheat oven to 400°F. Cream together the butter, sugar and vanilla. Slowly add the flour and salt and mix just until combined. Stir in the nuts.
Scoop into 1-inch balls and round them smooth between your hands. Bake 10-12 minutes, until cookies are set but not browned.
Remove from the oven and allow the cookies to cool on the tray for a minute or two and then roll each warm cookie in powdered sugar and set them a cooling rack.
Once the cookies have fully cooled, roll them once or twice more in powdered sugar. Store in an airtight container.
Video
Notes
The easiest method I've found for coating the cookies in powdered sugar is to put about a cup of powdered sugar in a bowl and roll the warm cookies, a few at a time, through the sugar.