- 3 pounds pork shoulder (Boston butt)
- 1 large white onion, halved through root end, plus chopped for serving
- 2 heads of garlic, halved crosswise
- 1 bay leaf
- 3 whole cloves
- 10 guajillo chiles, ribs and seeds removed
- 6 dried chiles de árbol, ribs and seeds removed
- Kosher salt
- 3 (15-ounce) cans white hominy, rinsed
- Thinly sliced cabbage, thinly sliced radishes, dried oregano, and lime wedges (for serving)
- Place pork shoulder, onion halves, garlic, bay leaf, and cloves in a large pot. Pour in 14 cups water (pork should be submerged). Bring to a simmer and cook, skimming as needed and turning pork occasionally, until meat is cooked through and tender but not yet falling apart, 2 1/2–3 hours. Transfer pork to a plate; let cool slightly. Strain broth into a large bowl, then transfer back to pot. Slice pork into 1/2″ slices and add to broth.
- Meanwhile, preheat oven to 350°F. Toast all the chiles on a rimmed baking sheet until brown (do not char) and starting to lightly puff in places, about 5 minutes. Bring 3 cups water to a boil in a medium saucepan; add chiles. Remove from heat and let chiles soak until softened, 10–12 minutes. Blend chiles and cooking liquid in a blender until smooth; season with salt.
- Add chile purée to pork and broth. Bring to a simmer, add hominy, and cook, skimming off fat from surface, until pork is so tender it’s nearly falling apart, 45–60 minutes; season with more salt.
- Divide posole among bowls, top with onion, cabbage, radishes, and oregano. Serve with lime wedges.
- Posole can be made 3 days ahead. Let cool; cover and chill.