1. Beat together butter and 1/2 cup confectioners sugar in a large bowl with an electric mixer at moderately high speed until pale and fluffy, about 4 minutes. Beat in vanilla, then add flour, pecans, and salt and mix at low speed until just combined. Chill, covered, at least 6 hours.
2. Preheat oven to 375°F.
3. Let dough stand at room temperature until just pliable, about 15 minutes. Roll level teaspoons of dough into 3/4-inch balls and arrange about 2 inches apart on lightly buttered large baking sheets.
4. Sift remaining 2 1/2 cups confectioners sugar into a large shallow bowl.
5. Bake in batches in middle of oven until bottoms are pale golden, 8 to 10 minutes. Immediately transfer hot cookies to confectioners sugar, gently rolling to coat well, then transfer to a rack to cool completely.
6. Roll cookies in confectioners sugar again when cooled.
7. Cooks' note: · Cookies keep in an airtight container at room temperature 3 weeks.