1. Combine pork, water, half the onion, 3 garlic cloves, bay leaves, and 2 teaspoons salt in a large pot. Bring to a boil, skim foam from the surface, then reduce to a gentle simmer. 2. Partially cover and simmer for about 1 1/2 hours, until the pork is beginning to become tender. 3. Meanwhile, toast guajillo and ancho chiles in a dry skillet for about 20 seconds per side. Cover with very hot water and soak 20 minutes. 4. Blend softened chiles with the remaining onion half, remaining 3 garlic cloves, oregano, cumin, and 1 cup pork broth until very smooth. Strain through a fine sieve. 5. Remove the cooked onion, garlic, and bay leaves from the pork broth and discard. 6. Stir the strained chile puree into the pot. Add the drained hominy. 7. Simmer uncovered for 45 to 60 minutes, until the pork is very tender and the broth is richly flavored. Add a little hot water if it becomes too concentrated. 8. Taste and adjust salt. Ladle pork, hominy, and broth into deep bowls. 9. Let each person garnish with cabbage, radish, onion, cilantro, lime, and a pinch of oregano. Serve with crisp tostadas.