Cut pork into large chunks, season generously with salt, and brown on all sides in a large pot or Dutch oven over medium-high heat. Add the quartered onion, peeled garlic cloves, and bay leaves to the pot, then cover with enough water or chicken broth.

Bring the liquid to a boil, then reduce heat to low, cover, and simmer for 2 to 3 hours, or until the pork is very tender and easily shreds. Carefully remove the cooked pork from the pot, shred it using two forks, and set aside.

Strain the cooking liquid into a separate bowl; discard the solids (onion, garlic, bay leaves), reserving the broth. While the pork cooks, remove stems and seeds from the dried Guajillo, Ancho, and Arbol chilies, then place them in a heatproof bowl.

Pour hot water over the chilies and let them rehydrate for about 20-30 minutes, until softened. Transfer the rehydrated chilies to a blender with about 1 cup of the reserved pork broth and blend until completely smooth.

Carefully strain the blended chili mixture through a fine-mesh sieve into a clean large pot or back into the cleaned Dutch oven, pressing firmly on the solids to extract all liquid, then discard the pulp. Bring the strained chili sauce to a simmer and cook for about 15 minutes, allowing it to thicken slightly and deepen in flavor.

Add the shredded pork back into the pot with the chili sauce, along with the drained and rinsed hominy. Pour in the remaining reserved pork broth, ensuring the hominy and pork are well submerged.

Stir in the dried Mexican oregano and ground cumin, then bring the mixture to a gentle simmer. Cook for another 20-30 minutes, allowing all the flavors to meld together and the hominy to fully heat through; adjust seasoning with more salt if needed.

Ladle the hot pozole into individual bowls. Serve with a variety of garnishes on the side, including thinly sliced radishes, shredded green cabbage, finely diced white onion, fresh chopped cilantro, and lime wedges for squeezing over.