Preheat oven to 375 and line a large baking sheet with parchment paper.
Heat a large pot or dutch oven over medium-high heat. When hot, add the pork, fat side down, to the skillet and sear until golden, 3 to 4 minutes.
Pour in enough water so that the pork is covered by one inch and bring to a boil. Once boiling, add 1 tablespoon of kosher salt and reduce heat to a rapid simmer and cook, covered, for 45 minutes.
Place the onion in a high-speed blender and add 3-4 ladles (about 1 cup) of the boiling water from the pot and blend until smooth. Pour into the stew pot. Cover and continue to simmer. (Keep the blender out, you’re going to need it a few more times).
Meanwhile, place the tomatillos and poblano peppers on the prepared baking sheet and drizzle with 2 tablespoons of olive oil. Toss to coat and transfer to the oven. Roast until the poblanos are tender and the tomatillos have softened, about 15 minutes.
Place the tomatillos and poblano peppers in the blender with 3-4 ladles of the liquid from the boiling pot. Blend until smooth and add to the stew. Cover and continue to cook.
Meanwhile, place the cilantro, green leaf lettuce, garlic with 3-4 ladles of the liquid from the boiling pot. Blend until smooth and add to the pot of stew.
Continue to simmer, covered, until the pork is very tender, about 2 - 2.5 more hours.
Using tongs, transfer the tender pork to a cutting board and cut into small, bite sized cubes and transfer back to the stew pot. Taste the stock and add more salt, as needed. The soup will need more than you think since it’s a very large pot of soup and you use water as the base to make the broth. Then, add the hominy (be sure to drain and rinse!) and continue to cook, covered, until the hominy is tender, about 20 more minutes.
When ready to serve, ladle the pozole into bowls and top with lettuce (or cabbage), sliced radishes, torn chiles (optional), cilantro, and serve with a lime wedge! Enjoy!