Heat the oven to 350°F and line two baking sheets with parchment. Beat butter and dough sugar until creamy, then mix in vanilla.
Mix in flour and salt just until combined, then fold in the finely chopped pecans. Divide the dough into 30 compact balls.
Place 1 inch apart and bake one sheet at a time for 13 to 14 minutes, until the bottoms turn pale gold and the tops look dry.
Cool for 5 minutes, then gently roll the warm cookies in the coating sugar. Set on a rack and cool completely.
Roll once more in the remaining powdered sugar, tapping off loose excess before storing.