Toast the chiles: Heat a dry skillet over medium heat. Toast the guajillo and ancho chiles for 2-3 minutes until fragrant, being careful not to burn them.
Soak the chiles: Place the toasted chiles in a bowl and cover them with hot water. Let them soak for 15 minutes until softened.
Sauce and Meat
Blend the sauce: Drain the soaked chiles and add them to a blender. Include garlic, onion, beef broth, cumin, oregano, apple cider vinegar, salt, and pepper. Blend until smooth.
Sear the beef: In a large pot, heat a drizzle of oil and sear the beef chuck roast on all sides until browned (about 8-10 minutes).
Add the sauce: Pour the blended sauce over the seared beef, ensuring it’s well-coated.
Braise: Cover the pot and lower the heat. Let it braise on the stove for about 3 hours, or until the beef is tender and easily shredded.
Finishing Touches
Prepare the consomé: Remove the beef from the pot. Shred the meat with two forks. Strain the liquid to create the consomé, discarding any solids.
Assemble the tacos: In a skillet, heat the corn tortillas until warm. Fill each tortilla with shredded beef and Oaxacan cheese. Fold and fry until crispy and the cheese melts.
Serve: Serve warm with a side of consomé for dipping, garnishing each plate with fresh cilantro and lime wedges.
Use fresh ingredients for enhanced flavor and consider marinating meat for additional depth. For a vegetarian version, substitute meat with jackfruit or mushrooms and use vegetable broth.