In a large saucepan or Dutch oven, combine chicken broth, carrot strips, leeks or onion, barley, the 1-1/2 teaspoons fresh or 1/2 teaspoon dried savory, the pepper, and salt. Bring to boiling; reduce heat. Cover and simmer about 15 minutes or until vegetables are tender.
Stir in half-and-half or light cream, turkey or chicken, and strained carrots. Heat through. If desired, garnish each serving with additional fresh savory. Makes 4 servings.