In a large pot, add the pork, halved onion, garlic cloves, bay leaves, and salt. Pour in water or broth to cover the meat and bring to a boil. Reduce to a gentle simmer and cook uncovered for about 1½ to 2 hours, or until the pork is tender and shreds easily. Skim off any foam as needed.
While the pork cooks, soak the dried chiles in hot water for 20 minutes until softened. Drain and transfer to a blender along with garlic, salt, and 1 cup of reserved cooking liquid or water. Blend until smooth. For a silky texture, strain the sauce through a fine mesh sieve to remove bits of skin and seeds.
Remove the cooked pork from the pot and shred it into bite-sized pieces. Discard the bay leaves and onion. Return the shredded pork to the pot. Stir in the chile sauce, oregano, and cumin. Simmer for another 15–20 minutes to let the flavors meld.
Add the drained hominy to the pot and cook for an additional 10–15 minutes, just to heat through. Taste and adjust salt if needed. You want a rich, balanced broth with a hint of spice.
While the soup finishes, prepare your toppings. Thinly slice the cabbage and radishes, chop the onions and cilantro, and cut your limes into wedges. Arrange everything in small bowls so everyone can customize their serving.
Ladle the hot pozole into bowls and let your guests add their favorite garnishes. A squeeze of lime, a sprinkle of oregano, and a handful of cabbage can completely transform the flavor. Serve with warm tortillas or crispy tostadas on the side.