Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a large mixing bowl, use an electric mixer on medium speed to cream together the softened butter and granulated sugar until the mixture is light and fluffy, about 2-3 minutes.
Beat in the vanilla extract, then gradually add the flour and salt, mixing on low speed just until the dough comes together and no dry streaks remain.
Fold in the finely chopped pecans with a spatula until they are evenly distributed throughout the dough.
Scoop 1 tablespoon of dough and roll it between your palms to form a 1-inch ball; repeat with remaining dough, placing balls 2 inches apart on the prepared baking sheets.
Bake for 12-14 minutes, or until the bottoms are lightly golden and the tops are still pale.
Let the cookies cool on the baking sheet for 5 minutes until firm enough to handle but still warm.
Place powdered sugar in a shallow bowl and roll each warm cookie in the sugar until fully coated, then transfer to a wire rack to cool completely.