Place the Guajillo and Ancho chiles in a bowl full of near-boiling water. Allow the peppers to soak for at least 30 minutes. While the peppers soak, season the chuck roast chunks with salt and pepper to taste.
Heat 1 tablespoon of oil in a large Dutch oven set over medium-high heat. In 2 batches, sear the roast on all sides, using more oil as needed. Transfer the seared chuck roast to a plate and set aside.
Add the remaining oil, tomatoes, onion, and garlic to the pot. Cook for 2-3 minutes. Pour in the beef broth to deglaze the pot. Transfer the hydrated chiles from the bowl of water to the pot. Add the short ribs, spices, and cinnamon stick. Bring the mixture to a boil, reduce the heat, and maintain a gentle simmer for 30 minutes.
Remove the short ribs and add to the plate with the seared roast. Skim the top of the pot to remove any impurities from the bone cooking out. Remove the cinnamon stick and discard. Transfer about 1 ½ – 2 cups of the braising liquid to a bowl. Cover the bowl and refrigerate. Use an immersion blender to blend the remaining pepper and tomato mixture until smooth.
Return the short ribs, seared beef, and any juices back to the Dutch oven. Add the orange juice, apple cider vinegar, salt, and pepper to taste. Bring to a simmer, cover, reduce heat to medium-low, and cook for at least 3-4 hours. When the beef is cooked through, remove the short rib bones. Shred the meat with 2 forks.