In a dry skillet over medium heat, toast the guajillo and ancho chilies for 2-3 minutes until fragrant, stirring occasionally to prevent burning. Once toasted, transfer the chilies to a bowl and cover them with hot water. Let them sit for 15 minutes, or until they soften.
After the chilies have softened, drain any excess water. In a blender, combine the softened chilies, garlic, quartered onion, ground cumin, ground coriander, oregano, black pepper, and 1 cup of beef broth. Blend until the mixture reaches a smooth, thick consistency.
In a large mixing bowl, season the beef chunks generously with salt. Pour the chili marinade over the beef, ensuring each piece is thoroughly coated. Cover with plastic wrap or a lid and refrigerate for a minimum of 2 hours, but ideally overnight for maximum flavor infusion.
In a large pot or Dutch oven, heat a couple of tablespoons of oil over medium-high heat. Once the oil is shimmering, add the marinated beef in a single layer and sear it on all sides until browned, which should take about 5-7 minutes.
Pour in the remaining beef broth and add the bay leaf. Bring the mixture to a boil, then reduce the heat to low. Cover the pot and let it simmer for 2-3 hours, or until the beef is tender enough to shred with a fork.
After the simmering time, remove the pot from heat. Take out the beef and shred it using two forks, taking care to break apart any large pieces. If desired, strain the cooking liquid to remove solids and then return the shredded beef to the pot to soak in the flavorful broth.
In a separate skillet, heat over medium-high heat. Lightly toast the corn tortillas for about 30 seconds on each side, making them pliable but not too crispy. Fill each tortilla with a generous amount of the shredded birria.
Arrange the filled tacos on a serving platter. Garnish with freshly chopped cilantro and diced onions. Provide lime wedges on the side for squeezing over the tacos for added brightness and flavor.
Notes
Serve with a bowl of broth for dipping and lime wedges for added flavor.