Cream together the butter and 1/2 cup powdered sugar until light and fluffy, then stir int he vanilla.
In a separate bowl, whisk together the flour and salt. Gradually beat this into the butter, then stir in the chopped nuts.
Divide the dough in half, then cover with plastic wrap and chill for 30 minutes to 1 hour.
Preheat the oven to 400 F.
Form the chilled dough into 1 inch balls, and place onto parchment lined baking sheets. They won't expand too much while baking, but leave about an inch between them.
Bake until the cookies begin to turn a light, golden brown, about 10 to 12 minutes.
Remove from oven and let cool slightly, until they're cool enough to handle, basically. Put the remaining powdered sugar in a shallow bowl or plate. Working with a few at a time, toss the warm cookies in the powdered sugar. Transfer to a wire rack to finish cooling.