In a large pot, simmer the pork shoulder in salted water for 2-3 hours, or until completely tender. Skim off any foam that rises to the surface.
While the pork is cooking, soak the guajillo and pasilla chiles in hot water for 15 minutes. Remove the stems and seeds. Blend the chiles with a little water until you have a smooth paste.
Remove the cooked pork shoulder from the pot and shred it into smaller pieces. Strain the cooking liquid and set it aside.
In a large pot, heat the chili paste, then add the beef broth, oregano, cumin, and bay leaves. Stir to combine and bring to a boil.
Add the hominy and shredded pork to the pot. Reduce heat to low and simmer for 30 minutes to allow the flavors to meld.
Before serving, prepare the garnishes: slice the lime and radishes, shred the lettuce, and chop the cilantro.
Serve the soup in deep bowls, topped with lime, radishes, cilantro, and lettuce. Sprinkle with a pinch of dried oregano, if desired.
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