Heat the oven to 350°F. Line two baking sheets with parchment paper.
Beat the butter and 1/2 cup of the powdered sugar with an electric mixer until light and fluffy, about 2 minutes. Beat in the vanilla.
Whisk the flour and salt in a medium bowl. Add to the butter mixture on low speed just until combined, then fold in the pecans.
Roll the dough into 1-inch balls (about 1 tablespoon each) and place 1 inch apart on the prepared sheets.
Bake 12-14 minutes, until the bottoms are lightly golden and the tops are still pale. Cool on the sheets 5 minutes.
Roll the warm cookies in the remaining 1 cup powdered sugar, set on a rack, and roll again once cool.