In a large, heavy saucepan or enameled cast-iron casserole, combine the pork, salt, pepper, cumin, oregano and chipotle puree (to control the spiciness, start with 1 tablespoon; you can always add more later). Add the liquid from the canned hominy along with the bay leaf and enough water to just cover the meat (about 2 cups). Bring the soup to a boil and skim off any foam that comes to the surface. Reduce the heat, add the finely chopped onion and cook the soup, covered, at a low simmer for 1 hour.
Add the hominy to the soup, turn the heat up a little and cook, uncovered, at moderately low heat until the pork is tender and the liquid has thickened slightly but is still soupy, about 50 minutes. (Posole is typically eaten with a spoon. If the soup becomes too thick, you can add water to recover that delicious broth.) Ten minutes before the soup is done, stir in the chopped garlic. Before serving, add the chopped cilantro.
Assemble dishes of cilantro leaves, diced onion, dried oregano, sliced radishes and diced avocado; let guests garnish their own steaming bowls of posole. Serve with the lime wedges (for squeezing over the posole) and the warm tortillas on the side.