Measure 16 cups water into a large pot. Add 1 onion, the meat and all the rest of the meat ingredients. Bring to a boil, cover and simmer 2 hours for pork, 3–4 hours for beef, or until meat is tender and falls from the bone. Half an hour before the meat is fully cooked, add the fresh or frozen nixtamal (but not canned).
While this is cooking, soak chilies for 15 minutes in just enough hot soup stock to cover. Place them in a blender with garlic and salt and all the liquid. Buzz to a smooth paste. Add more liquid if needed. In a large skillet heat oil, add the chile paste and fry, stirring constantly for 5 minutes, until thickened. Taste and add salt if needed. Remove from heat and set aside.
Remove meat with slotted spoon and cool at room temperature for 15 minutes. Remove bones and cut meat into bite-sized pieces. Return meat to cooking liquid. If you are using canned nixtamal add it now. Add red chile paste and the 2 chopped onions. Simmer gently for 30 minutes. Taste and adjust seasonings.
Prepare all condiments and arrange them on a wide platter. Put the oregano in a little bowl on the side. Ladle the posole into wide bowls for the diners and be sure they get full instructions and warm tortillas.