- Beat together butter and 1/2 cup confectioners sugar in a large bowl until pale and fluffy, about 4 minutes.
- Beat in vanilla.
- Add flour, pecans, and salt and mix until just combined.
- Chill the dough covered for at least 6 hours.
- Preheat oven to 375°F.
- 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 baking sheets.
- Bake in batches in middle of oven until bottoms are pale golden, 8 to 10 minutes.
- Sift remaining 2 1/2 cups confectioners sugar into a large shallow bowl. (To start, use less than 2 1/2 cups and add as needed.)
- Immediately transfer hot cookies to confectioners sugar, gently rolling to coat well.
- Transfer to a rack to cool completely.
- Roll cookies in confectioners sugar again when cooled.