Grandma's Cream of Chicken Soup

"Cook chicken (older hens have more flavor) not too much water (makes it weak). I add some celery, onion, and carrots, salt and pepper, after it has cooked a while when chicken is done - take chicken our of broth - cool and take chicken off bones - cut in small pieces. Put meat in broth and heat till it comes to a boil, mix corn starch or flour (to thicken) with water or cool broth. Should be fairly thick, I then add close to a pint of cream, or half&half (or half of each). Although I think the cream makes the soup. Maybe with one chicken a half pint of cream would be enough."