Prepare the Chilis: In a dry skillet over medium heat, toast the guajillo and ancho chilies until fragrant, about 2-3 minutes. Be careful not to burn them. Once toasted, transfer to a bowl and cover with hot water for about 20 minutes until softened.
Make the Sauce: Drain the chilies and place them in a blender along with cumin, oregano, garlic, and roasted onion. Add some of the beef broth to help blend everything smoothly, then blend until a thick paste forms.
Cook the Meat: In a large pot, combine the beef chunks, spice paste, remaining beef broth, bay leaves, salt, and pepper. Bring to a boil, then reduce to a simmer and cover. Cook for 2-3 hours, or until the meat is tender and easily shreds.
Shred the Beef: Once the meat is tender, remove it from the pot and shred it using two forks. Set aside. Strain the broth and reserve it for dipping (consommé).
Assemble the Tacos: Heat a skillet over medium-high heat. Take a corn tortilla, dip it briefly in the reserved broth to soften, then place it on the skillet. Add a generous amount of shredded beef and top it with a handful of Oaxaca cheese. Fold the tortilla in half and cook until the cheese melts and the tortilla is crispy, about 2-3 minutes on each side.
Serve: Remove from the skillet and sprinkle with fresh cilantro. Serve hot with lime wedges and a bowl of the reserved consommé for dipping.
Notes
For best results, use fresh tortillas and high-quality cheese.