Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or leave them ungreased.

In a large mixing bowl, using an electric mixer, cream together the softened butter and the ½ cup of powdered sugar until the mixture is light and fluffy. Beat in the vanilla extract until well combined.

In a separate medium bowl, whisk together the all-purpose flour and salt. Gradually add the flour mixture to the butter mixture, mixing on low speed until just combined. Do not overmix.

Stir in the chopped pecans or walnuts by hand using a wooden spoon or spatula until they are evenly distributed throughout the dough.

Shape the cookie dough into small balls, approximately 1 inch in diameter (about the size of a small walnut). Place the balls 1 to 2 inches apart on the prepared baking sheets.

Bake for 12 to 15 minutes, or until the bottoms are lightly golden brown. The cookies should remain pale on top.

Remove the cookies from the oven and let them cool on the baking sheets for 2 to 3 minutes. This allows them to firm up slightly before handling.

First Roll in Sugar: While the cookies are still warm, gently roll each cookie in a bowl filled with extra powdered sugar until completely coated. Place them on a wire rack to finish cooling.

Second Roll in Sugar: Once the cookies are completely cooled (this is essential for the snowy texture), roll them in powdered sugar a second time for a thick, characteristic coating.