Cover sun-dried tomatoes with boiling water to re-hydrate. Sauté garlic and green pepper with 1 tablespoon of oil until slightly softened. Add sun-dried tomatoes, Italian seasoning, and chicken broth; heat to boiling. Dissolve cornstarch in cold water. Add slowly to boiling broth mixture, stirring briskly to slightly thicken. Stir in chicken, cheese, and basil; heat gently until cheese is melted.