Prepare the Chiles: Start by placing the guajillo and pasilla chilies in a skillet over medium heat. Toast them for about 2-3 minutes until fragrant, then remove from heat and soak in hot water for about 15 minutes until soft.
Blend the Sauce: In a blender, combine the soaked chilies, minced garlic, chopped onion, cumin powder, oregano, black pepper, and 1 cup of beef broth. Blend until smooth, adding more broth as needed to reach a sauce-like consistency.
Cook the Beef: In a large pot or Dutch oven, add the beef chunks and pour the blended chili sauce over them. Add the remaining beef broth and bay leaves. Bring the mixture to a boil, then reduce to a simmer. Cover and cook for about 2.5 to 3 hours, or until the beef is tender and easily shreds with a fork.
Shred the Meat: Once the beef is cooked, remove it from the pot and shred it using two forks. Discard any excess fat and return the shredded meat back to the pot with the broth.
Prepare the Tacos: In a separate skillet, heat a little oil over medium heat. Dip each tortilla briefly in the birria broth, then place it in the skillet. Add a generous amount of the shredded beef to one half of the tortilla. Fold the tortilla over and cook until crispy and golden brown, about 2-3 minutes per side.
Serve: To serve, place the tacos on a platter and garnish with chopped cilantro and diced onion. Accompany with lime wedges for squeezing over the top.
Notes
Adjust salt to taste and serve with lime wedges for added flavor.