Generously season the meat with salt and pepper on all sides. Heat olive oil in a large pot or Dutch oven over medium-high heat.
Working in 2 batches, sear the meat on all sides until browned. Remove and set aside.
Add guajillo, ancho, arbol chiles, tomatoes, onion, cinnamon stick, bay leaves, and peppercorns to a medium pot. Cover with water, boil, then simmer covered for 10 minutes.
Transfer the softened items to a blender with 1 cup soaking water, beef broth, vinegar, garlic, cumin, oregano, and cloves. Blend until smooth.
Strain the blended sauce through a fine mesh strainer into the pot with the meat. Discard solids.
Stir meat and chile sauce to combine and bring to a boil. Reduce heat, cover, and simmer for 3 to 3½ hours until tender.
Transfer meat to a bowl and shred with 2 forks.
Return the shredded meat to the consommé. Stir and heat through.
Serve as stew or in tacos with diced onion, cilantro, and Oaxaca cheese if desired.