Preheat your oven to 375°F. (optional: line your baking sheet with parchment paper or a silpat)
In a large mixing bowl, beat together the butter and sugar until light and creamy
1 lb butter, 3/4 cup powdered sugar
Add the vanilla and mix well.
2 tsp vanilla
Stir in the flour, nuts and salt (if you are using it) until well combined.
4 cups flour, 2 cups walnuts, 1/2 tsp salt
Form the dough into small (~1"), smooth balls (I like to use a #100 cookie scoop to portion the dough) and place about 2 inches apart on your baking sheet.
Bake in your preheated oven for about 10-12 minutes. The cookies will puff up and spread just a little bit, the tops will be set and dry and the bottoms will be light golden brown. Transfer to a wire rack to cool.
Roll the cookies, a couple at a time, in powdered sugar until they are well coated. Store in a air tight container at room temperature.
additional powdered sugar for rolling
Notes
I don't believe mom did this, but I found that if I gave the cookies a quick roll in powdered sugar while they were still warm (almost hot), and then rolled them again after they had cooled I was able to get better coverage with the powdered sugar.
Mom always used margarine (salted), but I typically use unsalted butter so I added a bit of optional salt to the recipe.