In a large pot, heat 2 tbsp. of oil over medium heat. Add the pork shoulder pieces and cook until browned on all sides.
Remove the pork from the pot and set aside.
In the same pot, add the chopped onion and cook until softened.
Add the minced garlic and cook for 1 minute.
Toast the dried ancho chiles in the pot until fragrant.
Remove the chiles from the pot and blend them with 2 cups of chicken stock in a blender until smooth.
Add the pureed chiles back to the pot along with the dried oregano, cumin, thyme, flour, and remaining chicken stock.
Stir in the browned pork and bring the mixture to a boil.
Reduce heat and let the pozole simmer for 2 hours, stirring occasionally, until the pork is tender.
Stir in the drained and rinsed hominy and continue cooking for another 15 minutes.
Season with salt and pepper to taste.
Serve the pozole in bowls and top with shredded lettuce, sliced radish, diced onion, chopped cilantro, lime wedges, avocado, and crumbled queso fresco.