Bring broth to a boil in a large saucepan. Add onion, rice, and garlic. Cover; reduce heat to low. Simmer 20 minutes or until rice is tender, stirring occasionally. Add sorrel, salt, and pepper; cook, uncovered, 1 minute or until sorrel wilts.
Place yogurt in a bowl. Gradually add 3/4 cup broth mixture to yogurt, stirring constantly with a whisk. Stir yogurt mixture into remaining broth mixture in pan, and cook over low heat 1 minute or until thoroughly heated (do not boil). Ladle soup into bowls, and sprinkle with parsley, if desired.