Step 1: Preheat your oven to 400°F (200°C) and prepare a baking sheet with parchment paper or leave it ungreased.
Step 2: In a large mixing bowl, cream together the softened butter, 1/2 cup of powdered sugar, and vanilla extract until the mixture is smooth and light.
Step 3: Sift the flour and salt together, then gradually add to the butter mixture. Stir until a cohesive dough forms.
Step 4: Fold in the finely chopped walnuts until they are evenly distributed throughout the dough.
Step 5: Shape the dough into 1-inch balls by rolling small amounts between your palms. Place them on the prepared baking sheet about 1 inch apart.
Step 6: Bake for 10-12 minutes. The cookies should be set but not browned on top.
Step 7: Remove from the oven and let cool for 2-3 minutes. While still warm, roll the cookies in a bowl of powdered sugar.
Step 8: Transfer to a wire rack to cool completely. Once cold, roll the cookies in powdered sugar a second time for a thick coating.