Gather all your ingredients to make the process smoother.
In a large mixing bowl, cream together the softened butter and powdered sugar until light and fluffy, about 2-3 minutes. Add vanilla extract and mix well. Gradually add flour and salt, mixing until just combined. Fold in the chopped walnuts.
Scoop tablespoon-sized portions of the dough and roll them into balls, about 1 inch in diameter. Place on a baking sheet lined with parchment paper, spacing them about 2 inches apart.
Preheat your oven to 350°F. Bake the cookies for 12-15 minutes until the bottoms are lightly golden and the tops remain pale. Let them cool on the baking sheet for about 5 minutes.
While still warm, roll the cookies in additional powdered sugar. Allow to cool completely on a wire rack, and dust with more powdered sugar if desired.