Place pork shoulder, onion halves, whole garlic cloves, salt, pepper, and chicken broth in a large heavy-bottomed pot. Bring to a boil over high heat, then reduce to a gentle simmer and cook uncovered for 60–70 minutes, skimming foam as needed.

Meanwhile, remove stems and seeds from dried guajillo and ancho peppers. Toast the cleaned peppers in a dry skillet over medium heat for 30–45 seconds per side until fragrant.

Transfer toasted peppers to a bowl, cover with 1½ cups hot water, and soak for 10–15 minutes until softened.

Place tomatillos, serrano peppers, and jalapeño on a baking sheet. Broil 4–5 inches from heat for 8–10 minutes, turning halfway, until blistered and charred in spots. Let cool slightly.

Add soaked peppers with their liquid, roasted tomatillos and fresh peppers, cilantro, and chopped garlic to a blender. Blend on high until completely smooth, about 1–2 minutes.

Strain the blended sauce through a fine-mesh strainer into a bowl, pressing with a spoon to extract as much liquid as possible; discard solids.

When pork is fork-tender, remove it with a slotted spoon. Strain the cooking broth, discard onion and garlic solids, and return broth and pork to the pot.

Stir in the green sauce, drained hominy, and ground cumin. Taste and adjust seasoning with salt and pepper.

Simmer the pozole over low heat for 10–15 minutes to meld flavors. Keep heat gentle to prevent the hominy from breaking apart.

Ladle hot pozole into bowls and serve with shredded cabbage, radishes, lime wedges, tostadas, diced onion, cilantro, jalapeño slices, avocado, and a pinch of Mexican oregano.