In a Dutch oven or large stockpot over medium-high heat, combine the chicken carcass and drippings, 1 onion, 2 carrots, the garlic, and enough water to cover the chicken carcass by 2 or more inches, and bring to a boil.

Reduce the heat to low, cover, and simmer for at least 3 hours, and up to 12 hours.

Strain the broth through a sieve into a large pan.

Discard the chicken carcass and soggy vegetables.

In the same Dutch oven over medium heat, sauté the remaining half onion and 1 remaining carrot with the zucchini for about 5 minutes.

Add the cooked chicken, and pour the broth on top.

Simmer over low heat until ready to serve.