In a large pot, add 16 cups of water, bay leaves, 1 tsp salt, and chicken breasts.
Bring to a boil over medium heat, then reduce to a simmer and cook about 20 minutes, until the chicken is tender.
Remove chicken and let cool slightly.
Keep the broth in the pot as the soup base.
Once cool enough to handle, shred the chicken and set aside.
In a dry skillet over medium heat, roast tomatillos, jalapeño, poblano, Anaheim pepper, onion, and garlic until lightly charred and tender, about 10–15 minutes total, removing ingredients as they finish.
Transfer roasted vegetables to a blender with epazote (or radish greens) and cilantro.
Add about 1 cup of water and blend on high until completely smooth.
Pour the blended green sauce into the pot with the chicken broth.
Add shredded chicken, hominy, oregano, cumin, and chicken bouillon.
Stir well and bring to a gentle boil.
Once boiling, reduce the heat to a simmer and cook uncovered for about 20 minutes to let the flavors meld.
Taste and adjust seasoning or broth as needed.
Ladle pozole into bowls and top with cabbage, onion, radish slices, and lime juice.
Serve hot and enjoy.