Cut the pork off the bone in large chunks. Sprinkle salt and pepper liberally over all the chunks, including the bone. Pop the stems off the dried chiles and shake out the loose seeds.
Set a heavy 6-8 quart dutch oven over medium heat. Add the oil to the pot. Once hot add the pork chunks, including the bone. Brown the pork on all sides.
Move the pork to the sides of the pot. Add in the onion wedges and garlic. Sear for 1-2 minutes, then add in the chile peppers, bay leaves, oregano, 6 cups chicken broth, and 1 teaspoon salt. Push the chiles down under the liquid.
Cover the pot with a heavy lid and bring to a boil. Then lower the heat and simmer for 50-60 minutes, until the pork is soft enough to shred. (Keep the pot covered.)
Remove the pork chunks, bone, and bay leaves. Discard the bone and bay leaves. Use tongs or forks to shred the pork into small chunks.
Use an immersion blender to puree the vegetables, chiles, and broth into a thick sauce. You can also do this is a standard blender, but cover the lid with a towel, to protect against hot liquid splashing out.
Add the shredded pork back to the pot, along with the rinsed hominy. Stir to combine. If the sauce seems too thick add 1+ cup chicken broth or water to the pot.
Stir in the lime juice. Taste, then season with salt and pepper as needed. Keep warm until ready to serve.
To serve: Ladle the posole into bowls. Garnish the top with tortilla chips, sliced avocado, radishes, lime wedges, and cilantro.
Shredded cabbage or lettuce is also a traditional garnish, but I prefer it without.