Combine sugar, butter, and milk in a large saucepan; bring to a boil over medium heat. Cover and cook 2 to 3 minutes to wash down sugar crystals from sides of pan. Uncover and cook, stirring constantly, until a candy thermometer registers 234° (soft ball stage). Remove from heat, and add vanilla (do not stir). Let cool 10 minutes. Beat at medium speed with an electric mixer 6 to 7 minutes or until icing is spreading consistency.