Remove skin from chicken; set aside. In a 4-quart Dutch oven cook garlic in hot oil over medium heat for 15 seconds. Add chicken pieces. Cook about 10 minutes or until chicken is light brown, turning to brown evenly. Drain off fat. Add potatoes, carrots, celery, onions, broth, wine, snipped or dried rosemary, salt, and pepper. Bring to boiling; reduce heat. Cover and simmer for 35 minutes or until chicken is no longer pink (180 degrees F).
Transfer chicken and vegetables to a serving platter; keep warm. Measure cooking liquid; add water, if necessary, to equal 1 cup total liquid. For sauce, stir together the 2 tablespoons cold water and the cornstarch; stir into reserved liquid. Return to Dutch oven. Cook and stir over medium heat until thickened and bubbly. Cook and stir for 2 minutes more. Season to taste and serve with chicken. If desired, garnish with additional fresh rosemary.