Bring a medium-size saucepan of water to a boil. Lightly salt; add carrots and beans. Cook for 5 minutes, or until crisp-tender. Drain and set aside.
Meanwhile, heat 1 tablespoon of the oil in large nonstick skillet over medium-high heat. Season chicken with 1/2 teaspoon of the salt and the black pepper.
Add chicken and cook for 6 to 7 minutes, turning once, until chicken is cooked through. Remove to a plate and reserve.
Add remaining tablespoon of oil to skillet. Add onion, eggplant and garlic; cook for 7 minutes, until eggplant is tender. Add a few tablespoons of water to skillet as needed to prevent sticking. Stir occasionally.
Stir together broth, cornstarch, Italian seasoning, red pepper and remaining 1/2 teaspoon salt. Add to skillet. Stir in cooked carrots, beans and chicken. Bring to a simmer and add tomatoes. Cook until thickened and ingredients are heated through.
Stir in the basil and vinegar. Serve with cooked pasta or noodles, if desired. Makes 6 servings.