Beat butter, 1/2 cup sugar, and vanilla in large bowl with mixer until light an fluffy. Gradually add flour, beating on low speed after each addition until blended. Add nuts; mix well.
Shape dough into 48 1 inch balls. Place, 1 1/2 inches apart on baking sheets lined with parchment paper.
Bake 14 to 15 minutes or until bottom are lightly browned. Cool 5 minutes on baking sheets. Roll warm cookies, 1 at a time in remaining sugar in small bowl until evenly coated; place on wire racks. Cook completely.