Toast the guajillo, ancho, and chipotle chiles in a dry skillet over medium heat for 20 to 30 seconds per side, just until fragrant. Transfer them to a bowl and cover with hot water to soften for 15 minutes.

Meanwhile, heat the vegetable oil in a large pot or Dutch oven over medium-high heat. Season the beef with salt, then sear the chuck roast and short ribs in batches until browned on all sides. Remove and set aside.

In the same pot, add the onion, garlic, and tomatoes. Cook for 4 to 5 minutes until lightly browned and softened.

Drain the softened chiles and place them in a blender with the onion, garlic, tomatoes, beef broth, 1 cup water, cumin seeds, oregano, thyme, black pepper, cloves, vinegar, and 1 teaspoon salt. Blend until very smooth.

Pour the chile sauce through a fine mesh strainer into the pot for a smoother consomé, pressing with a spoon to extract as much liquid as possible.

Return the seared beef to the pot, then add the bay leaves, cinnamon stick, and enough remaining water to almost cover the meat. Bring to a simmer, cover, and cook on low heat for 3 to 3 1/2 hours, or until the beef is very tender and shreds easily.

Remove the beef from the pot and shred it with two forks. Discard the bay leaves and cinnamon stick, then taste the consomé and adjust salt if needed.

Heat a skillet or griddle over medium heat. Dip each tortilla lightly into the top layer of the consomé, then place it on the skillet. Add shredded beef and a little cheese to one half of the tortilla, then fold it over.

Cook the tacos for 1 to 2 minutes per side, until crisp, golden, and the cheese is melted. Repeat with the remaining tortillas, adding more oil to the skillet only if needed.

Serve the birria tacos hot with chopped onion, cilantro, lime wedges, and small bowls of warm consomé for dipping.