Add the dried hominy to a large bowl and cover completely with cold water to soak overnight.
1 1/2 pounds dried hominy
Drain hominy and transfer to a large pot. Cover with water and bring to a boil over medium-high heat. Reduce to medium-low and let simmer for 1 hour or just until the kernels have started to pop. Drain and set aside.
Meanwhile, lightly toast the dried chiles in a cast-iron skillet or dutch oven over medium-high heat until fragrant, about 3-4 minutes, turning occasionally. Remove from the skillet and transfer to a cutting board. Use kitchen shears to cut the chiles open and remove and discard the stems and seeds from the chiles. Transfer the chiles to a medium saucepan and cover with 4 cups of water. Heat to a simmer over medium heat, then simmer for 30 minutes. Transfer the softened chili peppers to a blender and blend into a smooth paste by adding as much of the reserved chili water as needed to get a consistency you like. I use about 1 cup of the soaking water from the chiles until it is about the consistency of a chimichurri sauce or thick milkshake. Set aside. This step can be done 1-2 weeks in advance and stored in the fridge or frozen for up to 3 months in the freezer.
10-12 dried red New Mexico chiles
Season the pork with the salt and pepper.
2-3 pounds boneless pork shoulder, 1-2 teaspoons kosher salt, 1/2 teaspoon black pepper
Heat the vegetable oil in a large dutch oven or pot over medium-high heat. Working in batches so as not to crowd the pan, sear the seasoned chunks of meat on all sides until nicely browned but not cooked through. Transfer the meat to a plate and set aside.
2 Tablespoons vegetable oil
Add the onion to the same pot and sautee for 3-4 minutes to soften slightly, scraping up any browned bits from the bottom of the pan. Add the garlic and cook for another 30 seconds.
1 large yellow onion, 6 cloves garlic
Return the seared pork to the pot along with the hominy and add the chicken broth, water, bay leaf, and oregano. Bring to a simmer, then cover and cook for 2 1/2 hours, adding water if needed, until the meat is fall-apart tender and the hominy has burst. Skim off any fat or foam from the top of the posole as it cooks.
8 cups chicken broth, 4 cups water, 1 bay leaf, 1 1/2 Tablespoons Mexican oregano
Stir in 1 cup of the chili puree and let the posole continue to simmer for another 15 minutes. Taste and adjust seasoning with additional salt and pepper or more of the chili puree, as needed.
Serve with diced white onion, fresh cilantro leaves, and lime wedges with corn or flour tortillas on the side for dipping into the posole. Some folks also like to serve queso fresco, thinly sliced green cabbage, thinly sliced radishes, sliced avocado, and Mexican crema for adding to the top of their bowls of posole. Personally I prefer to stick with just onion, cilantro, and lime.
Fresh cilantro leaves, diced white onion, and lime wedges