Step 1Heat the oven to 350 degrees.
Step 2In the bowl of a stand mixer, or in a large bowl using an electric mixer, beat the butter with one-half cup powdered sugar until light and fluffy. Beat in the vanilla.
Step 3In a separate bowl, whisk together the flour, salt and nuts. Beat the flour mixture slowly into the butter over low speed if using a stand mixer, or gently stir the flour into the butter mixture by hand until evenly combined to form a dough.
Step 4Roll the dough into 1 inch balls (about 1 rounded teaspoon of dough per cookie); if the dough is too soft to roll, chill it in the refrigerator until it is easy to handle. Place the cookies at least 2 inches apart on ungreased cookie sheets. Bake until lightly browned, about 15 minutes.
Step 5While the cookies are still hot, gently roll them once in the remaining powdered sugar, then place the cookies on a rack to cool. After the cookies have cooled, roll them again in the remaining powdered sugar.
Step 6Store the cookies in tightly sealed plastic bags; they also freeze well.