In a Dutch oven, sauté chilies in 1 tablespoon oil over medium heat until heated through, don't brown. Transfer chilies to a bowl; add boiling water. Soak them while you do the next step.
In the Dutch oven, brown pork in remaining oil in batches, sauteing onion and garlic with the last batch of pork. Return all pork to pan and add broth. Bring to a boil. Reduce heat; cover and simmer until meat is tender, 30 minutes. Remove and fork apart if desired.
Transfer chilies and their liquid and Roma tomatoes to a blender; cover and process until smooth. Press through a mesh strainer, reserving pulp and discarding skins/seeds. Add pulp to pork mixture. Stir in the pork, hominy (or garbanzo), bay leaves, chili powder, coriander, oregano and salt. Cover and simmer, 30 minutes.
Stir in lime juice and cilantro.
To serve, ladle into bowls. Optional: to garnish, spread a row of radishes around the curve of the bowl. Sprinkle red onions and cilantro on top. Place lime or lemon wedges and tortilla on plate next to the bowl.