In a large stockpot, combine the turkey carcass, water, broth and quartered onion. Bring to a boil over high heat.
Reduce heat, cover and simmer for 1 hour.
Strain the mixture, discarding the carcass and onion. Chill the liquid in the refrigerator overnight, if possible and skim off the fat from the broth's surface.
Return the liquid to the stockpot.
Add the remaining ingredients to the broth mixture. Bring to a simmer and cook, covered, for about 1 hour.
Ladle into individual bowls and serve immediately.