Preheat Oven: Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Cream Butter and Sugar: In a large mixing bowl, cream together the softened butter and 1/2 cup powdered sugar using an electric mixer until light and fluffy.
Add Vanilla: Mix in the vanilla extract until well combined.
Mix Dry Ingredients: In a separate bowl, whisk together the all-purpose flour and salt.
Combine: Gradually add the dry ingredients to the butter mixture, mixing until just combined.
Add Nuts: Fold in the finely chopped nuts.
Form Cookies: Scoop out tablespoon-sized portions of dough and roll them into balls. Place them on the prepared baking sheet, spacing them about 1 inch apart.
Bake: Bake in the preheated oven for 15-18 minutes, or until the bottoms are lightly golden.
Cool and Roll in Sugar: Allow the cookies to cool for a few minutes on the baking sheet, then roll them in powdered sugar while they are still warm. Let them cool completely on a cooling rack, and roll them in powdered sugar again for a final coating.