Using your hands (or scissors), remove the stems from the chilis and remove about half the seeds (or leave them all in if you are confident in your tolerance for spiciness). Tear (or slice/cut) the chilies and place in a medium saucepan over medium-high heat. Using tongs or a wooden spoon, toss the chilies occasionally, until they start to smell toasted, fruity, almost chocolate-y, about 2-3 minutes.
Add the chopped onion, about half the garlic, 3 cups of water and season with salt. Bring to a simmer and reduce heat to low, letting the chilies and onions/garlic soften in the water for 5 or so minutes. Transfer all the chilies, onion and garlic to a blender or food processor along with about half the liquid in the pot and blend until the mixture is mostly smooth; save the remaining water to use later and set both set aside.
Next, season pork with salt and pepper. Heat oil in a large, heavy bottomed pot over medium heat. Working in batches as needed, add pork and sear until deeply browned all over, about 12–16 minutes total. Transfer pork to a large bowl, leaving the fat behind and set aside.
Add remaining chopped or sliced garlic to your pot and cook over medium heat until lightly browned and toasted, 3–4 minutes. Add the chili paste and use a wooden spoon to scrape up the bits on the bottom of the pot.
Add the pork back to the pot, along with tomatillos, torn cabbage, any leftover water from the chilies and 5 cups of additional water. Season with salt and pepper and bring to a simmer. Reduce heat so it’s gently bubbling and let it do its thing, uncovered, for 2-ish hours, until the pork is cooked through and tender.
Add in drained hominy, season again with salt and pepper and continue simmering another hour or so, until the hominy has had a chance to become flavored by the broth.
Once the pozole is finished, serve and top with the sliced cabbage, onion, cilantro, tostadas, etc, serving with lime wedges alongside for squeezing over.
