Place the carrots, celery, onions and chicken broth in a large pot. Cook over medium high heat until tender, about 15 minutes. Mix the cornstarch with the butter until smooth and set aside.
In a separate pot heat the milk, but do not boil. Slowly add the cornstarch/butter mixture to the milk and stir together until smooth. Add this mixture to the vegetables and continue to cook over medium heat. Slowly add the cheese to the soup, stirring constantly, until cheese is melted. Serve hot or cold.