Place first 9 ingredients and 2-½ teaspoons salt in a 6- or 7-qt. slow cooker.
In a large bowl, mix egg and remaining ½ teaspoon salt. Add turkey; mix lightly but thoroughly. Shape into 1-¼-in. balls; drop gently into slow cooker.
Cook, covered, on low until vegetables and barley are tender, 6-8 hours.
