In a dry skillet or comal over medium heat, toast the guajillo, ancho, and chile de arbol (if using) for 2-3 minutes, pressing them down gently with tongs, until fragrant. Be careful not to burn them, as this will make the sauce bitter.

Transfer the toasted chiles to a bowl and cover them with hot water. Let them rehydrate for 20-30 minutes until soft.

While the chiles are rehydrating, in the same skillet, dry roast the halved Roma tomatoes for about 5-7 minutes until slightly charred.

Drain the rehydrated chiles, reserving about 1/2 cup of the soaking liquid. In a blender, combine the drained chiles, roasted tomatoes, the halved white onion and peeled garlic cloves (from the birria stew ingredients list, separate from taco topping onion), apple cider vinegar, and the reserved chile soaking liquid. Blend until completely smooth. If needed, add a little more beef broth or water to help it blend, but keep it thick.

Pat the beef chuck roast and short ribs dry with paper towels. Season generously with salt and pepper.

Heat 2 tablespoons of vegetable oil in a large Dutch oven or stockpot over medium-high heat. Sear the beef in batches until browned on all sides, about 3-4 minutes per side. Remove the seared beef and set aside.

Pour the blended chile sauce into the Dutch oven. Add the bay leaves, Mexican oregano, ground cumin, ground cloves, cinnamon stick, and the remaining salt and pepper. Bring to a simmer, stirring occasionally, for 5 minutes.

Return the seared beef to the pot. Pour in the beef broth until the meat is mostly submerged. Bring to a boil, then reduce heat to low, cover, and simmer for 3-4 hours, or until the meat is fork-tender and easily shredded. Alternatively, you can transfer to a slow cooker and cook on low for 6-8 hours.

Remove the meat from the pot and let it cool slightly. Skim off any excess fat from the surface of the stew; this rendered fat (consommé fat) is essential for dipping the tortillas when making the tacos. Strain the remaining birria stew through a fine-mesh sieve into a separate pot or bowl. Discard the solids. This flavorful broth is your consommé.

Shred the cooked beef using two forks. Discard any bones or large pieces of fat. Mix a little of the consommé with the shredded meat to keep it moist.

Heat a large skillet or comal over medium heat. Dip each corn tortilla into the reserved birria fat (the red oil skimmed from the top of the consommé), ensuring both sides are coated.

Place the fat-dipped tortilla on the hot skillet. Sprinkle a generous amount of shredded cheese on one half of the tortilla. Immediately add a spoonful of the shredded birria meat on top of the cheese.

Cook for 1-2 minutes until the cheese begins to melt and the tortilla is lightly crispy. Fold the tortilla over to form a taco. Press down gently with a spatula.

Continue cooking for another 1-2 minutes per side until the tortilla is golden brown and crispy, and the cheese is fully melted. Repeat with the remaining tortillas, cheese, and meat.

Serve the Birria Tacos hot with small bowls of the warm consommé for dipping. Garnish with finely diced white onion, chopped cilantro, and lime wedges.