Place the chicken, carrots, celery, onions, fennel, bay leaf, garlic, and parsley stems in a large soup pot and cover with cold water by 1 in/2.5 cm. Bring to a boil over high heat, then turn the heat to low. Gently simmer, partially covered, skimming off any foam that accumulates, until the chicken is very tender and falling off the bone, 1 to 1-1/2 hours. You want the soup to roll along at the gentlest simmer. If it starts to bubble too vigorously, nudge the heat down a little.