Toast the chiles. Heat a dry skillet over medium-high. Toast the guajillo, ancho, and árbol chiles per side until fragrant and pliable — do not let them blacken or they'll turn bitter.
Soften and blend. Cover toasted chiles with hot water; soak . Char the onion halves, garlic, and tomatoes in the same dry skillet until blistered, . Drain chiles (reserve soaking liquid) and blend with the charred vegetables, oregano, cumin, peppercorns, cloves, vinegar, and 1 cup soaking liquid until smooth. Strain through a fine-mesh sieve.
Sear the beef. Season chuck and short ribs aggressively with salt. Sear in a Dutch oven over high heat in batches until deeply browned, per side. Set meat aside.
Braise. Pour the chile sauce into the pot and cook, stirring, until darkened and thickened, . Return the meat with any juices. Add beef stock, cinnamon, bay leaves, and salt. Bring to a boil, then cover and transfer to a 325°F oven. Braise until the meat shreds with a fork.
Shred and strain. Remove the meat to a bowl; shred with two forks, discarding bones and large fat pieces. Strain the consommé through a fine sieve into a wide bowl, skim excess fat from the top (reserve a few tablespoons for griddling), and stir 1 cup of consommé back into the shredded meat.
Build the tacos. Heat a griddle or skillet over medium-high. Dip each tortilla briefly in the reserved consommé fat, lay on the griddle, and top with cheese and shredded beef. Fold in half and griddle per side until the cheese melts and the tortilla crisps.
Serve. Plate tacos with chopped onion, cilantro, and lime wedges. Pour the warm consommé into small bowls for dipping.