Place the chicken in a large pot and pour the broth over it, adding water if necessary to cover the chicken completely. Cover the pot and bring to a boil. Lower the heat and simmer until the chicken is tender, about 1 hour. Remove the chicken from the pot and refrigerate it and the broth, preferably overnight.
Skim the top layer of fat off the broth. Remove the chicken from the bones, shred, and add to the broth. Add the onion, scallions, carrots, celery, parsnips, zucchini, cabbage, tomatoes, parsley, dill, pepper, and paprika. Bring to a boil, lower the heat, partially cover, and simmer until the vegetables are just tender, about 30 minutes. Add the noodles and cook until tender, about 5 minutes.