Remove fat from chicken. Put chicken in a large casserole or pot.
Add parsnip, celery, onion, bay leaves, thyme and small pinches of salt and pepper. Cover ingredients with water.
Bring to a boil. Skim foam from surface.
Cover and cook very low heat 1½ hours.
Add carrots, garlic and zucchini, bring to a simmer. Cover and cook over low heat about 30 minutes or until the chicken is cooked through and the vegetables are tender.
Skim off fat. Remove and discard the parsnip, bay leaves and thyme springs.
Remove skin from chicken. Carve chicken into serving pieces and return them to soup. Taste and adjust seasoning.
Serve chicken in fairly shallow bowls with carrots and zucchini. Add dill, cilantro or parsley in each bowl.
Moisten each serving with a few spoonfuls of soup.