Cream butter in a large mixing bowl. Add the vanilla then gradually add the 1/2 cup confectioners' sugar, beating until light and fluffy. Sift the flour, measure, then sift again with the salt. Add gradually to the butter mixture. Add the pecans and mix well.
Shape the dough into 1-inch balls and place 2 inches apart on ungreased baking sheets. Flatten slightly using the bottom of a glass, then bake for 20 minutes, or until edges are very lightly browned. Remove the cookies from the baking sheets and roll in powdered sugar while still hot. Cool on wire racks and roll cookies again in powdered sugar before serving.
Once they are completely cooled, cookies may be stored in airtight containers for up to 1 week.