Remove the stems and seeds from the guajillo and ancho chiles. Cover with hot water and soak for 15–20 minutes until pliable. Quarter the onion and peel the garlic on a clean board. On a separate board, cut the fully thawed chuck into large chunks. Drain and discard the soaking water.
Blend the softened chiles, quartered onion, garlic, Mexican oregano, whole clove, vinegar, salt, and 1 cup of the cool beef broth until smooth. Strain through a fine-mesh sieve if there are visible bits of chile skin or clove.
Put the beef in a 6-quart slow cooker. Pour over the chile sauce and add the remaining 2 cups of broth. Cover and cook on LOW for about 8 hours, keeping the lid closed, until the beef shreds easily with forks. If it resists, continue on LOW and check again in 30–60 minutes. Check that the stew reaches at least 165°F with a food thermometer.
Transfer the beef to a board and shred it. Stir in just enough cooking liquid to keep it moist. Let the remaining liquid settle for a few minutes, skim the red surface fat into a small dish, and keep the remaining consommé hot. Taste the broth and adjust its salt.
Heat a 12-inch skillet over medium heat. Lightly coat a tortilla with the reserved red fat and lay it in the skillet. Add one-sixteenth of the shredded Oaxaca cheese and beef to one half, fold, and cook for about 2–3 minutes per side until browned and crisp and the cheese has melted. Work in batches. If too little fat separates, lightly brush the tortilla with red cooking liquid and add a thin film of neutral oil to the skillet; do not soak the tortilla.
Serve two hot tacos per portion with warm consommé for dipping. Add diced onion, cilantro, and lime if using; serve the tacos as soon as they leave the skillet.