Place the chicken, water, halved onion, garlic, bay leaves, salt, and peppercorns in a pot. Bring up slowly over medium heat until just below a boil. Skim off the foam and impurities as they rise. Lower to a very gentle simmer and cook 35–45 minutes, until the chicken is fully tender and cooked through. The meat should pull away easily from the bone but not be falling apart into threads yet. Remove the chicken to a tray. Strain the broth and discard the solids. You should have around 1.4–1.6L broth. When cool enough to handle, remove skin and bones and shred the chicken into bite-size strands. Keep the broth at a gentle simmer, never a hard boil, so it stays clean and clear in flavor rather than cloudy and flat. This clean, clear broth carries directly into every later stage of the dish — it's used to blend the verde base, thin the fried sauce, and build the finished pozole, so protecting its clarity here matters far beyond this first stage alone.

While the chicken cooks, roast or blister the tomatillos, poblanos, serranos, jalapeños, chopped onion, and garlic on a tray under a broiler or in a dry skillet/comal. Turn as needed until the tomatillos soften and blister, the chiles char in spots, and the onion and garlic take on some color. Place the poblanos in a bowl and cover for 5 minutes, then rub off most of the loose charred skin. Remove seeds only if you want a milder final pozole. The serranos and jalapeños can be left as they are, with seeds removed only if you want less heat. Toast the pumpkin seeds in a dry skillet over medium heat for 2–4 minutes, stirring often, until fragrant and lightly puffed. Do not let them darken too much or they can turn bitter. The pepitas should smell nutty and aromatic, not browned hard. The tomatillos should lose their raw sharpness. Covering the roasted poblanos to steam for those few minutes loosens their charred skin considerably more effectively than trying to peel it right off the heat — trapped steam softens the skin's grip on the flesh beneath it.

In a blender, combine the roasted tomatillos, poblanos, serranos, jalapeños, onion, garlic, toasted pepitas, cilantro, epazote or oregano, and 250ml hot broth. Blend until very smooth, adding a little more broth as needed. The mixture should be pourable but still fairly thick. If using parsley or spinach for color support, add it here in a small amount only. Blend long enough that the pepitas are fully broken down. The sauce should look smooth and vivid green, not gritty. Blending with the broth's own hot liquid, rather than water, means this base carries genuine chicken flavour built directly into it from this very first stage, rather than starting from something neutral.

Heat the lard or oil in a clean pot or the same pot over medium heat. Pour in the green puree carefully. It may sputter. Stir and cook 8–10 minutes, until it darkens slightly, smells fully cooked, and thickens a bit. This step deepens the flavor and removes the raw blended taste. The sauce should go from raw and sharp to mellow, savory, and rounded. This active frying stage is what actually transforms the blended purée into something genuinely cooked and integrated — that transformation doesn't happen automatically once the sauce is later diluted with more broth, which is exactly why it needs this dedicated stovetop time first.

Add the hominy to the cooked green sauce. Pour in about 1L of the chicken broth and bring to a gentle simmer. Add the shredded chicken and simmer 20–25 minutes so the hominy absorbs the broth and the flavors come together. Add more broth as needed during simmering. Pozole Verde should be brothy, not as thick as a stew or pipián. Taste and adjust salt. Add the lime juice only if the broth needs a final lift. The finished pozole should have a light body from the pepitas, but still enough broth to clearly surround the hominy and chicken in the bowl. This simmer gives the hominy real time to absorb some of the surrounding broth's flavour while staying suspended in a genuinely brothy liquid — the goal is body from the pepitas, not thickness from over-reduction.

Ladle the pozole into bowls. Top each serving with shredded cabbage, radish slices, diced avocado, and a lime wedge on the side. Serve immediately while the broth is hot and the garnishes stay cool and crisp. Adding every garnish only at the moment of serving, rather than into the simmering pot, is what preserves their genuinely cool, crisp, fresh character against the hot broth beneath them.