In a medium pot, bring about 2 cups of water to a boil.

Place the ancho, guajillo, and arbol chiles (seeded) in a heatproof bowl. Pour the hot water over the peppers and let them soak for at least 20 minutes.

Turn your broiler on HIGH and place the top rack in your oven about 6 inches from the heating element.

Place the halved tomatoes and quartered onion on a baking sheet that is lined with foil. Place under the broiler (6 inches) for about 4 to 5 minutes. Open the oven and add the garlic cloves and broil for another 4 to 5 minutes. Keep an eye on them, they should become soft and lightly charred. Don't let them burn (broilers vary, so do keep an eye on it). Remove from oven and set aside.

Sprinkle the roast pieces and short ribs with salt and pepper.

Heat the olive oil In a large Dutch oven or oven-safe pot (with a lid) over medium heat. Working in batches, sear the beef until browned all over. Repeat with remaining beef and then add it all back into the pot.

Use a slotted spoon to transfer the softened chiles into the blender (save the soaking liquid). Next, add the tomatoes, onion, and garlic. Add 1 tsp salt, the cumin, oregano, allspice, bay leaves, peppercorns, white vinegar, 1 cup of the chili soaking liquid, and 2 cups of beef broth (you may need to do this in 2 batches). Pureé until smooth (about 1 to 2 minutes).

Strain the pepper sauce through a fine-mesh colander, discarding any solids.

Pour the strained sauce over the meat and add more beef broth if necessary. The beef should be almost completely covered.

Bring the sauce to a boil. Cover and turn the heat to LOW and simmer until the meat is shreddable, usually 2 to 2½ hours. Check periodically and add more liquid (broth or water) if necessary. Be sure the meat is not sticking to the bottom of the pot and burning.

Remove the beef from the sauce/consommé and place on a cutting board. Discard bones and excess fat. Use two forks to shred the meat. Sprinkle salt over the top of the shredded meat (about 1 tsp).

Heat a medium skillet over medium-high heat. Working one at a time, dip a tortilla into the consommé/sauce and fully coat it. Add to the hot skillet and twist it around a bit so it won't stick. Working quickly, add about 1 tbsp cheese on one side of the tortilla and then top with a handful of the beef. Top with more cheese and then very carefully bring the open side of the tortilla over the meat and cheese. Cook on one side for about 1 minute, then flip and cook on the other side for another minute. The taco will be dark in color, and somewhat soft. Transfer to a baking sheet and keep warm in a low-temperature oven (250°F) and continue with the remaining tortillas.

If desired, skim the fat from the top of the consommé, or pour the sauce into a fat separator. Divide the consommé into individual ramekins or dipping bowls.

Serve the warm tacos with consommé on the side and garnished with chopped cilantro, onion, and hot sauce on the side.