Toast the Chiles: In a dry skillet over medium heat, toast guajillo and ancho chiles until fragrant, about 1-2 minutes. Soak them in hot water for 10 minutes to soften.
Blend the Sauce: In a blender, combine softened chiles, chipotle pepper, onion, garlic, tomato paste, cumin, oregano, cinnamon, cloves, and 1 cup of beef broth. Blend until smooth.
Sear the Meat: In a large pot or Dutch oven, heat vegetable oil over medium-high heat. Season the beef with salt and pepper, then sear on all sides until browned.
Combine and Simmer: Pour the blended sauce over the meat, add the remaining beef broth and apple cider vinegar. Stir well. Bring to a boil, then reduce heat to low. Cover and simmer for 2.5 to 3 hours, until the meat is tender and shreds easily.
Shred the Meat: Remove the meat from the pot and shred with forks. Reserve the cooking liquid as the consomé (dipping sauce).