Bring 8 cups of water to a boil in a 6-quart stockpot.
Meanwhile, lightly roast the dry chiles in a cast iron skillet over medium-high heat, about 2 minutes. Bring 1 1/2 cups water to a boil in a medium saucepan; add roasted chiles. Cover and let stand 15 to 20 minutes or until softened. Drain the chiles, reserving 1 cup of the soaking liquid.
While the chiles are soaking, heat the olive oil in the same cast iron skillet over medium-high heat. Sprinkle the pork with 1 tablespoon of the salt. Add 1/3 of the meat to the skillet. Cook until well browned, stirring and turning occasionally. Remove to the large pot of boiling water. Repeat with remaining meat in batches, adding 2 of the garlic cloves during the last batch.
Add all the pork to the large pot. Add a little of the boiling water to the skillet and scrape up the browned bits; add to the large pot.
Add the hominy, 1 tablespoon of the salt, bay leaves, oregano and cumin. Bring the mixture to a boil. Reduce the heat and simmer for 15 minutes.
While the pozole is cooking, place the softened chiles, remaining 2 garlic cloves, 1/4 cup of the soaking water and 1 teaspoon salt in blender container. Cover and blend on the high setting for 5 seconds. Remove the center cap from blender lid and add the remaining 3/4 cup of liquid with the machine running; blend 10 seconds or until smooth. (If any bits won’t blend, strain the mixture.)
Add the chile sauce to the pork and hominy. Return to a simmer. Simmer, partially covered, for 2 to 2 1/2 hours or until the pork is fork-tender.
Top the individual servings with a large dollop of sour cream. Then top with limes, avocados, cilantro, onion, cabbage, and radishes as desired. Serve with the tostada shells.