Cut pork shoulder into 1½ to 2-inch cubes.

Set aside ½ onion for the broth (roughly chopped is fine).

Keep the remaining 1 onion for roasting/toasting with the chiles.

Use 10 garlic cloves total, split between broth and sauce.

Add cubed pork, ½ onion, a handful of garlic cloves, and enough water to cover the pork by 1–2 inches to a large pot.

Bring to a gentle boil, then immediately reduce to a steady simmer.

Skim impurities for the first 15–20 minutes.

Add bay leaves, Mexican oregano, and salt.

Simmer 1 to 1½ hours, until the pork is tender.

Remove stems and shake out most seeds from the dried chiles.

Heat a dry skillet over medium and toast the guajillo + ancho chiles for 10–20 seconds per side.

In the same skillet, add the remaining onion and garlic and char/toast until onion has browned edges and garlic has a few dark spots.

Ladle 2–3 cups of hot pork broth into a blender and add toasted chiles, toasted onion + garlic, Mexican oregano, and a good pinch of salt.

Blend until very smooth and strain through a fine mesh sieve into a bowl.

Once pork is tender, add rinsed hominy to the pot and pour in the red chile sauce.

Bring back to a simmer and cook for 30 minutes to 1 hour.

Remove pork chunks to a bowl and shred with two forks.

Return the pork to the pot and simmer another 30 minutes if possible.

Taste and adjust salt and oregano as needed.

Serve hot with lime wedges, sliced radish, chopped cilantro, shredded cabbage or lettuce.