In a dry skillet over medium heat, toast the guajillo and ancho chiles for about 2-3 minutes until fragrant. Then, soak them in hot water for 20 minutes until softened. Drain and blend with 1 cup of beef broth until smooth.
In a large pot or Dutch oven, heat a splash of oil over medium-high heat. Season the beef chuck and short ribs with salt and pepper, then brown them on all sides (about 5-7 minutes). Remove the meat and set aside.
In the same pot, add the chopped onion and minced garlic, sautéing until soft and fragrant (about 3-4 minutes).
Return the browned meat to the pot. Pour in the blended chile sauce, remaining beef broth, apple cider vinegar, cumin, oregano, and cinnamon. Stir to combine everything well.
Bring the mixture to a simmer, cover, and reduce heat to low. Let it cook for about 2-3 hours, or until the meat is tender and easily pulled apart.
Once cooked, remove the meat and shred it using two forks. Return it to the pot, mixing it well with the broth.
Warm the corn tortillas in a pan or directly over an open flame. Fill each tortilla with a generous amount of the birria meat.
Serve the tacos accompanied by a small bowl of the broth for dipping. Top with chopped cilantro and diced onion.