Place a dry skillet over medium heat. Toast the prepared guajillo and ancho chiles for 30–60 seconds on each side, just until aromatic. Transfer the toasted chiles to a bowl, submerge them in hot water, and allow them to soften for 30 minutes.

Add the rehydrated chiles to a blender along with the halved white onion, garlic, Roma tomatoes, apple cider vinegar, oregano, cumin, and ground cloves. Pour in 1 cup of the liquid used to soak the chiles. Blend on high speed until the adobo mixture is completely smooth.

Blot the beef chuck pieces dry with paper towels, then season them liberally with salt and freshly ground black pepper. Warm the vegetable oil in a large skillet over medium-high heat. Brown the beef thoroughly on every side until a deeply caramelized crust forms, working in batches when necessary.

Arrange the seared beef in a 6-quart or larger slow cooker. Pour the blended adobo over the meat, then add the bay leaves and cinnamon stick. Stir to distribute the sauce and seasonings. Cover and cook for 8–10 hours on Low or 4–6 hours on High.

When the beef is exceptionally tender and separates easily, lift it from the slow cooker and shred it with two forks. Carefully skim the red-colored fat from the top of the braising liquid and reserve it in a separate bowl. Keep the remaining liquid in the slow cooker as the consommé.

Set a nonstick skillet or griddle over medium heat. Dip a corn tortilla into the reserved fat so both surfaces receive a light coating, then place it onto the heated skillet. Arrange shredded beef and shredded cheese over one side of the tortilla. Fold the tortilla in half and cook for 2–3 minutes on each side, until the exterior is crisp and the cheese has fully melted.

Serve the birria tacos immediately while hot and crisp, accompanied by small bowls of warm consommé for dipping. Finish the tacos and consommé with finely diced white onion, chopped cilantro, and a squeeze of fresh lime.