Soak the dried guajillo and ancho chiles in hot water for about 15 minutes until they soften. Once softened, drain and set aside.
In a large pot or Dutch oven, heat a bit of oil over medium-high heat. Add the beef chunks and sear until browned on all sides. Remove the beef and set aside.
In the same pot, add the chopped onion and sauté until translucent. Add minced garlic and sauté for another minute.
Place the softened chiles, cumin seeds, oregano, black pepper, and salt in a blender. Add 1 cup of water and blend until smooth. Strain the sauce through a strainer back into the pot to remove any solids.
Return the beef to the pot, along with the bay leaves and remaining water. Bring to a boil, then reduce the heat to low and let it simmer for about 2 hours, or until the meat is tender.
Once cooked, remove the bay leaves and shred the beef using two forks. Stir the shredded meat back into the pot.
Serve the Birria hot in bowls, garnished with chopped onion and cilantro, along with warm tortillas on the side.
Optionally, serve the broth separately for dipping the tortillas.