Step 1Place the meat in a large pot. Cover with water and bring to a boil. Boil 1 minute. Drain, discarding the water. Rinse the pot. Return the meat to the pot and add water to cover (12 to 14 cups depending on the pot).
Step 2Add the onion, garlic, bay leaves, salt and peppercorns. Bring to a boil, reduce the heat, cover loosely and boil gently until the meat is very tender, about 2 hours. Skim the surface as needed.
Step 3When the meat is tender, add the potatoes, corn, carrot, green beans, oregano, marjoram and thyme. Cover loosely and boil gently until the potatoes are tender, about 20 minutes.
Step 4Taste the broth and add more salt if needed. Add the zucchini and cook just until tender. Do not overcook or the zucchini will become soft and fall apart.
Step 5Serve in large soup bowls, spooning meat, some of each vegetable and broth into each bowl. Garnish with a cilantro sprig or a dash of chopped cilantro. Serve Mexican rice on the side. Accompany with hot salsa or sliced jalapenos and a bowl of Mexican limes.