**Prepare the Chiles for the Marinade:** Begin by removing the stems from all the dried chiles (guajillo, ancho, arbol). For the larger guajillo and ancho chiles, make a slit down one side and remove as many seeds as possible. You don't need to be perfect, just get the majority out. The arbol chiles can be left whole. Place all the prepared chiles into a medium heat-proof bowl.
**Rehydrate the Chiles:** Bring about 4 cups of water to a boil in a saucepan. Once boiling, carefully pour the hot water over the chiles in the bowl, ensuring they are fully submerged. Place a small plate or lid on top of the chiles to keep them under the water. Let them soak for at least 20-30 minutes, or until they are soft and pliable. This step is crucial for developing deep flavor.
**Prepare the Beef:** While the chiles are rehydrating, pat your chuck roast and short ribs dry with paper towels. Season all sides generously with salt and black pepper. You want a good coating here to build flavor. This drying helps with the next step, searing.
**Sear the Beef:** Heat a large Dutch oven or heavy-bottomed pot over medium-high heat. Add 1-2 tablespoons of olive oil. Once the oil is shimmering, carefully add the beef in batches, making sure not to overcrowd the pot. Sear each piece for 3-4 minutes per side, until a deep golden-brown crust forms. This browning adds immense flavor (the Maillard reaction!). Remove the seared beef and set aside.
**Assemble for Slow Cooking:** Return the seared beef to the Dutch oven. Pour the strained chile marinade over the beef, ensuring itās well coated. Add the beef broth and the whole peeled tomatoes (crushing them lightly with your hand before adding). Stir everything together. The liquid should mostly cover the meat. If it doesn't quite, add a little more beef broth or water.
**Slow Cook the Birria:** Bring the mixture to a gentle simmer on the stovetop. Once simmering, reduce the heat to low, cover the Dutch oven tightly, and cook for 3-4 hours, or until the beef is fall-apart tender. You should be able to shred it easily with two forks. Alternatively, you can transfer the covered Dutch oven to a preheated oven at 300°F (150°C) and cook for the same duration. Check it periodically; if it seems to be drying out, add a bit more broth or water. You want it swimming in that glorious sauce.
**Prepare Taco Toppings:** Finely dice the white onion and chop the fresh cilantro. Place them in separate small bowls, ready for topping your tacos. These fresh elements cut through the richness beautifully.
**Fold and Crisp:** Once the cheese is melty, fold the other half of the tortilla over the beef and cheese to form a taco. Press down gently with a spatula. Continue to cook for another 2-3 minutes per side, flipping once, until both sides are nicely crispy and golden brown. You want that perfect crunch! Repeat with the remaining tortillas, beef, and cheese.