Start by de-stemming and de-seeding the dried chiles. Give the chile pieces a quick roast in a 400F oven for 1-2 minutes. Alternatively, you can flash roast them in a skillet on the stovetop for 15-30 seconds per side. Cover the chile pieces with hot tap water and let them reconstitute for 20-30 minutes or until you need them.
Preheat your soup pot to medium high and add a glug of oil. Cut the pork shoulder into chunks in the 1-1.5" range. I usually trim off and discard any large pieces of fat. Sprinkle generously with salt and sear the pork pieces in the soup pot until turning brown on all sides (tongs work great for this step). Set the seared pork aside until you need it.
Finely chop an onion and add it to the soup pot along with another glug of oil. Cook over medium heat until softened (5-7 minutes) and then add 6 minced garlic cloves. Briefly cook the garlic. Scoop about half of this onion-garlic mixture into a blender where it will become part of the chile puree, and leave the other half in the soup pot.
Add 8 cups of stock to the pot along with the drained and rinsed hominy. I used a single 28 oz. can of hominy for this batch and that will make your Pozole a little more brothy. For a chunkier Pozole you can double the amount of hominy and use two cans.
Before draining the chiles be sure to take a taste of the soaking liquid. If you like the taste then you can use it to make the chile puree. If it tastes bitter to you then discard it and use stock to blend the chiles (that's what I did for this batch).
Drain the chiles and add them to the blender. Half of the onion-garlic mixture should already be in the blender. Add 2 cups of stock and combine well.
Add the chile puree to the soup pot. You can optionally strain it before adding it to the pot, but I usually blend it fine and skip that step. Straining it will remove any unwanted seeds or bits of skin, but it won't alter the flavor.
Add the seared pork pieces to the pot, along with any leftover juices that accumulated while they were waiting around.
Add the remaining spices to the pot: 1 tablespoon Mexican oregano, 1/2 teaspoon cumin, a pinch of ground clove, some freshly cracked black pepper, and 1 teaspoon salt. Stir well and bring to a simmer. Lower heat to maintain a simmer, cover, and let simmer for approximately 2 hours or until the pork is fall apart tender.
Once you're happy with the tenderness of the pork you can use two forks to shred it into bite-sized chunks, then returning it to the pot and mixing it in well. At this point you can optionally skim off and discard any fat that has accumulated on the surface (I usually trim off excess fat before searing the pork pieces, but then let the remaining fat become part of the Pozole.)
Take a final taste for seasoning. I added another pinch of salt and more Mexican oregano to this batch. Keep in mind that salt level will depend on which stock you're using.
Serve immediately with your choice of garnish. I kept this batch simple and topped with cilantro, crispy tortilla strips, and a squeeze of lime. Other good options include: thinly sliced cabbage or Iceberg lettuce, sliced radishes, raw onion, and sliced avocado.
Store leftovers in an airtight container in the fridge where it will keep for a few days. To reheat simply add Pozole to a saucepan over medium heat and cook until simmering. If it seems thick when re-heating I will add a splash of stock (or water) to thin it out.