Prepare the broth: In a large pot, add the chicken, water, onion, garlic, salt, black peppercorns, and bay leaf. Bring to a boil over medium-high heat. Skim off any foam that forms on the surface. Reduce heat to low, cover, and simmer for 45 minutes to 1 hour until the chicken is tender.

Remove the chicken: Take the chicken out of the pot and let it cool slightly. Shred the meat, discarding the bones and skin. Strain the broth if desired to remove onions, garlic, and peppercorns.

Cook the vegetables: Add carrots, potatoes, corn (if using), and chopped tomato to the broth. Simmer for 15 minutes until the vegetables are tender.

Add the zucchini and shredded chicken: Return the shredded chicken to the pot along with the zucchini, oregano, and lime juice. Cook for another 5 minutes.

Adjust seasoning: Taste and add more salt if needed. Stir in fresh cilantro just before serving.

Serve hot: Ladle into bowls and serve with warm tortillas, avocado slices, lime wedges, and optional cooked rice.