1. Cook the chicken, covered, until tender in the water with the celery, bay leaf, onion, salt and peppercorns, about 2 hours. Strain, reserving the meat. Remove the skin and bones and discard. Add the cream and milk to the broth and heat to a boil.
2. Cream the butter and flour together, add to the soup and cook, stirring, until the mixture boils.
3. Add the chicken meat and reheat. Garnish as desired with chopped parsley, watercress, shredded ham, sliced celery, toasted slivered almonds or cubed avocado.