Steps

1. Cook the corn. The most careful cooks like to remove the hard, pointy end — the germ — of each lime-treated corn kernal (nixtamal) so that the kernels will splay into a rough flower shape as they cook. A fingernail or small knife works well for this job, along with a lot of patience. (This step is impractical when using American Southwestern dried pozole corn.)
2. Measure 6 quarts of water into a large (10-quart or so) pot and add the corn (either the rinsed nixtamal or the dried corn) and garlic. Bring to a boil, partially cover the pot, and simmer gently over medium-low heat until the corn is thoroughly tender — at a minimum, allow 2 to 3 hours for nixtamal, about 5 hours for dried corn. Add water as necessary to keep the water level more or less constant. Slower, longer cooking only means better pozole, as evidenced by the fact that in many places in Mexico huge pots of the fragrant mixture simmer over wood fires overnight before a fiesta.
3. Cook the meat. While the corn is simmering, place all the meats in another large pot, cover with 4 quarts of water, add 2 tablespoons salt, and bring to a boil. Skim off the grayish foam that rises during the next few minutes, then add half the chopped onions. Partially cover the pot and simmer over medium-low heat until all the meat is thoroughly tender, about 2 hours. Remove the meat from the broth and let cool. Or, if time allows, cool the meat in the broth for the best flavor and texture, then remove it.
4. Skim the fat from the broth; you’ll have 2 generous quarts broth. Pull the meat from the pork shanks and pull the shoulder meat into large shreds. Cut the bones and knuckles out of the trotters. Discard the bones and knuckles, then chop what remains into ½-inch pieces. Add to the shredded meat (there will be about 6 cups meat in all). Cover and refrigerate if not serving within an hour.
5. Season the pozole. While the corn and meat are cooking, rehydrate the ancho chiles in enough hot water to cover (lay a small plate on top to keep them submerged) for about 20 minutes. Purée the chiles, liquid and all, in batches if necessary, in a blender or food processor.
6. When the corn is tender, press the chile mixture through a medium-mesh strainer (this removes tough chile skins) directly into the simmering liquid. Add the pork broth and 1 tablespoon salt, partially cover, and simmer for 1 hour.
7. Serve. When you’re ready to serve, set out bowls of the condiments for your guests to add to their steaming, fragrant bowlfuls: the lime wedges, sliced cabbage or lettuce, sliced radishes, oregano, and optional ground chile. Scoop the remaining chopped onion into a strainer, rinse under cold water and shake off the excess, then place in a bowl and set out with the other condiments.
8. Add the meat to the simmering pozole and check the consistency. It should look hearty — chock full of hominy, with bits of meat — but brothy enough to be thought of as a soup or brothy stew. If necessary, add water. Taste the pozole and season with additional salt if you think it’s necessary; since hominy soaks up a surprising amount of sat, you may need as much as another tablespoon.
9. Either serve your posole extravaganze (brothy stew plus garnishes and go-withs) buffet-style or ladle portions of the pozole into large soup bowls and deliver them to your guests, then pass around the condiments.
10. Before sprinkling it over the bowl, each guest should powder the whole-leaf oregano by rubbing it between his or her palms. The crushed red chile is for those who really like spice. The tostadas are eaten as an accompaniment on the side.