Place the chicken in a medium-large pot and add the water, halved onion, garlic cloves, bay leaves, peppercorns, and 2 tsp salt. Bring to a gentle boil over medium heat, then immediately lower to a very gentle simmer. Skim off any foam that rises during the first 10–15 minutes. Simmer for 30–35 minutes, or until the chicken is fully cooked and tender. Remove the chicken and set it aside until cool enough to handle. Strain the broth and discard the solids. You should have a clean, lightly golden broth. The broth should taste clearly of chicken and aromatics, but still clean and light. It should not be cloudy or greasy. Skimming diligently in that early window, when the most concentrated release of foam and impurities happens, is what sets this broth's clean, light character for the rest of the cook.

Once the chicken is cool enough to handle, remove and discard the skin and bones. Shred the meat into medium bite-sized strands. Set the shredded chicken aside. Do not shred the chicken too finely. Caldo Tlalpeño should have visible, generous strands of chicken that stay distinct in the soup. Keeping the strands genuinely substantial, rather than shredding down to fine threads, protects the chicken's own texture and presence in the finished bowl — overly fine shreds tend to disperse and lose their distinct identity once stirred into the broth and simmered further.

In a blender, combine the tomatoes, the chopped onion, the 2 garlic cloves, the chipotle chiles, the adobo sauce, and the dried oregano. Blend until smooth. Heat the oil in a pot over medium heat. Pour in the blended mixture carefully and cook for 8–10 minutes, stirring occasionally, until it darkens slightly, thickens a little, and loses its raw tomato smell. If using epazote, add it now. This stage matters. The tomato-chipotle mixture should be properly cooked before the broth is added. If it still smells raw and sharp, the finished soup will taste flat and harsh. This active cooking stage is what transforms the blended mixture from raw, sharp-tasting purée into a genuinely developed flavour base — that transformation simply doesn't happen once the base is diluted into the much larger volume of broth that follows, which is exactly why it needs to happen fully here, first.

Pour the strained chicken broth into the cooked tomato-chipotle base and stir well. Bring to a gentle simmer. Add the carrots first and cook for 10 minutes. Then add the chickpeas and zucchini. Simmer for another 8–10 minutes, until the carrots are tender, the zucchini is cooked but not collapsing, and the chickpeas are fully warmed through. Add the shredded chicken back to the pot and simmer for 3–4 minutes more, just until heated through. Taste and adjust with more salt as needed. Add 1 tbsp fresh lime juice, or to taste. The broth should be golden-red, lightly smoky, and brothy — not thick like a sauce. The vegetables should stay intact and distinct rather than melting into the soup. Returning the chicken to the pot only near the very end, after the vegetables are already close to done, is what keeps it from overcooking during this final simmering stage — it was already fully cooked during the initial broth-making, so it only needs to be reheated through here, not cooked further.

Ladle the soup into bowls. Top each serving with diced avocado and crumbled queso fresco. Serve with lime wedges on the side and, if you like, a little fresh cilantro. Serve immediately while the broth is hot and the avocado stays fresh and cool against the soup. The final bowl should have contrast — hot smoky broth, tender chicken, soft chickpeas, fresh avocado, salty queso fresco, and bright lime. Adding the avocado and queso fresco only at the very moment of serving, rather than into the simmering pot, is what preserves their genuinely fresh, cool, distinct character against the hot broth — either ingredient would soften and lose that contrast if it spent any real time simmering.