Pre-heat oven to 350°F.
Using a medium mixer bowl, cream the butter with 1/2 cup of the confectioners' sugar and the vanilla.
Mix in the flour, pecans, and salt.
Roll about 1 tbsp., or so, of dough into balls and place on an ungreased cookie sheet.
Bake in pre-heated oven until bottoms are golden, about 15 minutes.
Do not allow these cookies to get too brown: it's better to undercook them than to overcook them.
While cookies are still hot, roll them in confectioners' sugar.
Once they have cooled, roll them in confectioners' sugar once more.
Variation: sometimes for Christmas, Grandma would also add some crushed candy canes; add finely crushed candy canes to the confectioners' sugar used for the final dusting.