In a large pot, heat vegetable oil over medium heat. Add onions and garlic, sauté until translucent.
Add beef tripe and pork shoulder, cook until browned.
Stir in diced tomatoes, oregano, cumin, salt, and pepper. Cook for another 5 minutes.
In a separate pot, boil dried chilies in water for 10 minutes. Drain and blend with a cup of broth until smooth.
Pour chili mixture into the pot with meat. Add remaining broth and bay leaf. Bring to a boil, then reduce heat and simmer for 1.5 to 2 hours, until meat is tender.
Stir in hominy and simmer for another 30 minutes.
Adjust seasoning if needed. Serve hot with lime wedges and chopped cilantro.