Preheat your oven to 325°F (165°C) and line a baking sheet with parchment paper.
In a medium mixing bowl, use an electric mixer to cream together the softened butter and granulated sugar on medium speed until the mixture is light and fluffy, about 2-3 minutes, then beat in the vanilla extract.
Gradually add the flour and salt to the butter mixture, stirring with a spatula or mixing on low speed just until a soft dough forms, then fold in the finely chopped pecans until they are evenly distributed.
Scoop the dough by the tablespoon and roll it between your palms to form 1-inch balls, then place them about 1 inch apart on the prepared baking sheet.
Bake the cookies for 18-20 minutes, or until the bottoms are just lightly golden and the tops are set but not browned.
Let the cookies cool on the baking sheet for 5 minutes until they are firm enough to handle but still warm, then roll each one in the powdered sugar to coat completely.
Transfer the sugar-dusted cookies to a wire rack to cool completely, then roll them in powdered sugar a second time for a thick, snowy coating.
