Place the chicken carcass, onion, garlic, celery, carrots, red bell pepper, thyme, and bay leaves into a large stockpot.

Add enough water to cover the ingredients by about 1 inch.

Bring the mixture to a boil, then reduce the heat to low, cover with a lid, and let it simmer for 1 to 3 hours. The longer it simmers, the more flavorful the broth will be.

With about 15 minutes left in the cooking time, remove and discard the chicken bones, bay leaves, and thyme sprigs. Shred any remaining meat and return it to the pot.

Stir in the frozen peas and chopped zucchini, and continue to simmer for the remaining 15 minutes.

Season the soup with salt and pepper to taste, then serve warm.