In a large bowl mix together butter, confectioner's sugar, and vanilla until well incorporated.
In a medium bowl, sift together flour and salt. Stir into butter mixture. Add walnuts and mix.
Roll dough into 1 inch balls. Place on un-greased cookie sheets. They don't spread so they don't need to be spaced far apart.
Bake for 10-12 minutes. Let cool for a minute or two, then add another 1/4-1/2 cup of confectioner's sugar to a small bowl and then roll just out of the oven balls in sugar (don't worry, they wont fully coat, yet). Let cool and then roll again to get the full sugary coating.
Butter: If using salted butter, just omit the salt.