Put the pork shoulder piece(s) in a large kettle. Don't bother to cut them up. Cover with cold water, about 10 cups. Slowly bring to a simmer, uncovered. As it simmers for the first 10 minutes or so, skim off any scum that rises to the surface. (It will stop appearing after this.)
Simmer, partially covered, for at least two hours. Don't let too much water boil away; just leave the lid a bit ajar so a small amount of steam can escape.
Remove from heat. Remove the pork pieces from the broth and cut the meat from the bones. Discard the bones. Cut the meat in medium chunks (size appropriate for stew) and return it to the broth.
Crush or mince the garlic. Add the hominy with its juice, garlic, chili powder and salt to the pork and broth. Adjust the chili powder to your taste. The estimate here is for a mild store-bought unblended spice and will produce a mild pozole. If you grind your own chiles, they may be hotter. If you use a blend of chili powder and other spices (which is not recommended), you will probably want to reduce the salt. Remember that chili powder becomes mellowed and less spicy as it cooks.
Return to heat and simmer (partially covered as before) for another two hours. By this time, some of the meat will still be in chunks, and some will be shredded. Skim the grease from the top; there may be quite a bit. Check for salt before serving. (Don't try to add anything else at the end; chili powder and garlic need time to cook.)
Serve this with corn tortillas, wrapped in foil and warmed in the oven for ten or fifteen minutes.
NOTES: A simple New Mexican holiday stew -- This stew is from New Mexico. It is traditionally served on special days, such as Christmas Eve or New Year's Eve.
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