In a 6 quart stock pot over medium heat, add olive oil and pork pieces (in 2 separate batches). Cook until brown and set aside. Cook onion and 2 garlic cloves for 2-4 minutes until soft, adding more oil if necessary. Add pork, broth, hominy, oregano and bay leaves to pot and simmer over medium heat for 20 minutes. Spoon off any excess fat.
While pot is simmering, toast chilies in a skillet over medium heat for 30-45 seconds until soft. Transfer them to a bowl and cover with boiling water. Soak for 15 minutes until soft. In a blender, add chilies with a little soaking liquid, 1 clove garlic and a pinch of salt. Puree until smooth paste. Add chili puree to the pot and cook 5-10 more minutes. If too thick, add more liquid. Add chopped cilantro, lime juice, and salt to taste.
Serve family style with the serving pot of pozole in the middle of table or serve in individual bowls and let everyone garnish with their favorite toppings. Serves 4-6.