Finely chopped herbs, such as parsley, scallions, dill or a combination
1. Place the chicken, celery, carrots, onions, parsley, peppercorns, bay leaves and salt in a large soup pot and cover with cold water by 1 inch.
2. Bring to a boil over high heat, then immediately reduce the heat to very low. Adjust the heat to simmer and cook uncovered, until the chicken is very tender and falling off the bone, 1 to 1 1/2 hours.
3. When cool enough to handle, use tongs to transfer chicken from the pot to a container. Taste the broth and continue to simmer it until it is concentrated and tasty. Strain broth into a separate container.
4. Refrigerate chicken pieces and broth separately for at least 8 hours (or up to 3 days)
5. When ready to finish the soup, use your fingers to separate chicken breast meat from bones and skin. Discard bones and skin. Use two forks to pull the breast meat apart into soft chunks, or use a knife and cut into bite-size pieces. Reserve dark meat for another use.
6. Skim chicken fat from top of broth. Pour broth into pot with carrots and heat to a simmer. Add noodles and simmer until heated through, soft and plumped with chicken broth. Add the breast meat, then taste broth and add salt and pepper to taste. For best flavor, soup should have a few golden droplets of fat on top; if needed, add some chicken fat one teaspoon at a time.
Serve immediately, sprinkling each serving with herbs.