Creaming Process: In a large bowl, utilize an electric hand mixer to cream together the butter, 1/2 cup of powdered sugar, and 1 teaspoon of vanilla extract until the mixture achieves a smooth consistency.
Incorporating Flour and Salt: Gradually add the flour and salt to the creamed mixture, continuing to mix until the flour is fully integrated and no streaks remain. The resulting mixture will exhibit a lumpy texture. Use a firm spatula to fold in the toasted walnuts, ensuring they are evenly dispersed throughout the mixture.
Shaping the Dough: Proceed to shape the dough into balls, each approximately 1 inch in diameter. For consistency and ease, a small cookie scoop can be employed to portion the dough. Place the formed balls on the prepared baking sheet, maintaining a minimum distance of 1 inch between each ball. Bake in the preheated oven for a duration of 12 to 15 minutes, or until the base of the balls begins to display a golden coloration.
Coating with Powdered Sugar: Prepare a bowl containing 1 cup of powdered sugar. While the cookie balls are still notably warm, roll them in the sugar, ensuring a thorough coating. Following this, transfer the coated balls onto a platter to cool completely.
Final Sugar Coating: Once the cookies have reached room temperature, undertake a second rolling in powdered sugar to achieve a fully coated, snowball-like appearance. For storage, the cookies may be placed in an airtight container, where they will remain suitable for consumption for up to 1 week.