Remove stems and seeds from dried chiles, wipe clean, and soak in boiling water for 20-25 minutes until soft.
Place pork, onion, garlic, bay leaves, and water in a large pot. Bring to a boil, skim foam, reduce heat, and simmer for 1.5 to 2 hours until tender.
Remove pork from broth, let cool, then shred into bite-sized pieces. Discard onion, garlic, and bay leaves from the broth.
Blend softened chiles with garlic, onion, oregano, cumin, salt, and reserved pork broth until smooth. Strain the sauce into the pot of broth.
Add the shredded pork and drained hominy to the broth. Simmer gently for 30-45 minutes to meld flavors. Season with salt to taste.
Prepare garnishes: shred cabbage, slice radishes, dice onion, chop cilantro, and cut limes into wedges.
Ladle hot pozole into bowls and serve immediately with all garnishes on the side for everyone to customize.