Place the chicken pieces in a large pot. Add the onions, carrots, celery, garlic, parsnip, fennel, mushrooms, bay leaves, and salt. Add the water and bring to a boil. Use a large spoon to skim the scum off the top of the soup. Add the peppercorns and salt. Cover the pot, reduce the heat to low, and let the soup simmer, checking after 5 minutes and skimming off any additional scum. Add the parsley and dill, cover, and simmer for 2 hours. Let cool. Strain through a large sieve. Taste the soup and add more salt or pepper if necessary.