In a large soup pot, put chicken pieces, broth, parsnips, carrots, celery, onions and salt and pepper. Add water to cover chicken, if necessary.
Bring to a boil, then reduce heat and simmer for 1 hour. Add frozen peas.
Mix Bisquick and cream together. Drop by spoonfuls onto boiling soup. Reduce heat, cook for 10 minutes, uncovered. Cover and cook 10 minutes more or until dumplings are done.
Meanwhile, cook 2 cups egg noodles in boiling, salted water 8-10 minutes or to desired doneness. Drain.
Remove dumplings to a plate with a slotted spoon. In each soup bowl, place some of the noodles. Top with 2 pieces of the chicken and some of the soup. Add 2 dumplings to each bowl and garnish with parsley, if desired.