Prepare the Chilies: In a dry skillet over medium heat, toast the guajillo and ancho chilies for approximately 2-3 minutes, stirring occasionally until they become fragrant. Once toasted, place the chilies in a bowl and cover them with hot water. Allow them to soak for about 20 minutes until they soften.
Make the Sauce: After draining the softened chilies, transfer them to a blender. Add the ground cumin, dried oregano, minced garlic, and quartered onion. Pour in a small amount of the beef broth to facilitate blending. Blend the mixture until it achieves a thick and smooth paste.
Cook the Meat: In a large pot, combine the beef chunks, the prepared spice paste, the remaining beef broth, bay leaves, and season generously with salt and pepper. Bring the mixture to a boil over high heat, then reduce the heat to a simmer and cover. Allow it to cook for 2-3 hours, or until the beef is fork-tender and easily shreddable.
Shred the Beef: Once the meat is tender, remove it from the pot and place it on a cutting board. Shred the beef using two forks until it is finely shredded. Set the shredded beef aside. Strain the cooking broth through a fine mesh sieve, reserving it for dipping.
Assemble the Tacos: Heat a skillet on medium-high heat. Take one corn tortilla and briefly dip it in the reserved broth to soften it, then place it on the skillet. Generously fill the tortilla with shredded beef and top it with a handful of Oaxaca cheese. Fold the tortilla in half and cook until the cheese fully melts and the tortilla turns crispy, approximately 2-3 minutes per side.
Serve: Carefully remove the tacos from the skillet. Sprinkle them with freshly chopped cilantro for garnish. Serve hot with lime wedges on the side and a bowl of the reserved consommé for dipping.
Notes
For best results, use Oaxaca cheese or mozzarella for a great melt.