Notes: In lieu of posole use 3 to 4 cans (each about 14 1/2 oz.) hominy, rinsed and drained. Add only 4 cups water to the soup, and add hominy after meat is tender. Make this dish up to 3 days ahead, cool, cover, and chill. It thickens, so thin with more broth or water when reheating.
3/4 to 1 pound dried posole or 2 pounds soaked dried posole
1 1/4 pounds boned, fat-trimmed pork shoulder (butt) or shoulder end of pork loin
4 cups chopped onions
8 cloves garlic, minced
1 tablespoon dried oregano
1 can (49 oz.) or 6 cups reduced-sodium chicken broth
Rinse dried posole and let stand in 3 quarts water at room temperature at least 8 hours or up to 1 day. Drain.
Cut meat into 1/2-inch cubes.
In a 5- to 6-quart pan, combine pork, onions, garlic, oregano, and 1/2 cup broth. Cover and bring to a boil over high heat; reduce heat to medium and boil 20 minutes. Uncover and cook over high heat, stirring often, until juices evaporate and meat is sizzling in browned drippings, 15 to 20 minutes. Add 3/4 cup broth, stir browned bits free, and boil until liquid evaporates, then stir pork until it's lightly browned, 10 to 15 minutes.
Add remaining broth, 5 cups water, and drained posole; stir drippings free. Bring to a boil, then cover and simmer until pork is almost tender to bite, about 1 1/2 hours; stir occasionally.
Add 1/2 cup red chili sauce, 1/3 cup poblano chilies, and pepper. Simmer, covered, until pork and posole are very tender to bite, 15 to 30 minutes longer. Stew should be soupy; if needed, add more water to thin. Add salt and additional red chili sauce and poblano chilies to taste.