Preheat the oven to 350°F. Line a cookie sheet with parchment paper or leave it ungreased.
Using an electric mixer, cream together the butter and ½ cup confectioners’ sugar until light and fluffy. Beat in the vanilla. Add the flour and salt, and mix until well combined. Stir in the chopped pecans.
Form the dough into 1-inch balls (about 1 tablespoon each) and place them 2 inches apart on the prepared cookie sheet. Bake for 12 to 15 minutes, or until the edges are just starting to brown.
While the cookies are still warm, roll them in the remaining confectioners’ sugar. Let them cool, then roll a second time or dust the tops with sugar using a strainer. Cool completely before storing.