Escarole, radish, cilantro, and oregano for garnish
Toast and deseed the dried chiles and soak in warm water for 10 minutes.
Cut the pork shoulder into 1-inch cubed pieces and season lightly with salt.
Heat the canola oil in a large sauté pan. When hot, add the pork in several batches and cook until well browned on each side. Transfer to a separate plate.
After cooking the pork, drain the excess oil. Add in onion, garlic, and tomato. Sauté until slightly caramelized.
Transfer the pork and vegetables into a 4-inch-deep half hotel pan or deep roasting pan.
Drain the chiles. Add chiles to a blender with a little bit of the chicken stock. Purée until smooth. Add this mixture along with the rest of the chicken stock into a pot and bring to a boil, then pour stock over the pork shoulder.
Tightly foil the top of the hotel pan and cook in a 300-degree oven until pork is tender, around 1½ hours.
While pork is braising gather and prepare the ingredients for the second part of the recipe (see vegetables below).
When pork is tender, strain mixture through a chinois strainer, reserving the liquid for second part of recipe. Pick out all of the pork and discard the vegetables. When pork is cool enough to handle, pull apart into smaller pieces. Proceed to the second part of the soup.
In a soup pot, sweat down the peppers, onion, garlic, hominy, oregano, and cumin until soft, about 10
Measure the reserved braising liquid and skim off any excess fat on top. Add extra chicken stock until the mixture reaches 3 quarts. Add the stock and pulled pork into the pot and bring to a simmer. Cook for 25 minutes at a very low simmer.
Add in lime juice and most of the salt. Taste the stew for seasoning before adding in all of the salt.
A serving size is 1 cup, garnished with escarole, radish, cilantro, and oregano.