Season beef chunks and short ribs generously with salt and pepper.
In a dry skillet over medium heat, toast guajillo, ancho, and árbol chiles for 2 minutes until fragrant but not burnt.
Place toasted chiles in a bowl of hot water and soak for 15 minutes until softened.
In a blender, combine soaked chiles, halved onion, garlic, tomatoes, vinegar, cloves, oregano, cumin, and ginger. Blend until a smooth adobo paste forms.
Heat vegetable oil in a large Dutch oven over medium-high heat. Sear beef in batches until deeply browned on all sides, then remove meat.
Pour the adobo paste into the pot and cook for 3 minutes, stirring constantly to release aromatics.
Return meat to the pot. Add beef broth, cinnamon stick, and bay leaves. Ensure the meat is mostly submerged.
Bring to a boil, then reduce heat to low. Cover and simmer for 3 to 3.5 hours until meat is fork-tender and shreds effortlessly.
Remove meat from the pot, discard bones and bay leaves, and shred with two forks. Stir a ladle of the cooking liquid into the meat to keep it moist.
Skim the red fat (birria oil) from the surface of the cooking liquid and reserve in a small bowl. Strain the remaining liquid and keep warm as consommé.
Heat a flat griddle or non-stick skillet over medium heat. Dip a tortilla into the reserved red fat, coating both sides, and place on the griddle.
Top half of the tortilla with shredded cheese and a portion of shredded beef. Fold the tortilla and press down with a spatula.
Fry for 2 minutes per side until the tortilla is crispy and the cheese is fully melted.
Serve tacos immediately with individual bowls of consommé topped with fresh cilantro and diced onion for dipping.