Bring 1 gallon of water to a boil in your largest pot. Add the beef tripe and reduce the heat to a simmer. Let it cook for 2 hours, skimming off the fat periodically.

Drain the water completely and replace it with a fresh gallon. Return the tripe to the pot and simmer for an additional 2 hours.

Drain once more and add the final gallon of water. Bring the mixture back to a boil and add the garlic, chopped onion, salt, ground black pepper, dried oregano, ground red pepper, chile de árbol peppers, and japones chile peppers. Allow these flavors to meld by simmering for an additional 30 minutes.

Stir in the drained hominy and cook briefly until all the ingredients are well combined. Transfer the soup to bowls and let everyone garnish their serving with chopped onions, fresh cilantro, lime wedges, extra crushed red pepper flakes, and dried oregano. Serve with warm corn or flour tortillas on the side.