01 - Heat a dry skillet over medium heat. Toast guajillo, ancho, and pasilla chiles for 1-2 minutes until fragrant, flipping frequently. Transfer to a bowl, cover with hot water, and soak for 15 minutes until softened.
02 - In the same skillet, roast quartered onion, garlic cloves, and halved tomatoes until slightly charred, about 5 minutes. Set aside.
03 - Drain soaked chiles and transfer to a blender. Add roasted vegetables, vinegar, oregano, thyme, cumin seeds, peppercorns, cloves, and 1 cup beef broth. Blend until completely smooth.
04 - Heat vegetable oil in a large Dutch oven over medium-high heat. Pat beef chuck and short ribs dry. Sear meat on all sides until deeply browned, working in batches if necessary.
05 - Pour blended sauce over browned beef. Add remaining beef broth, bay leaves, cinnamon stick, and 2 teaspoons salt. Bring to a boil, then reduce heat to low. Cover and simmer for 2.5 to 3 hours until meat pulls apart easily.
06 - Remove beef from cooking liquid. Shred with two forks, discarding bones and excess fat. Skim surface fat from consommé and reserve 2-3 tablespoons for tortilla preparation.
07 - Preheat oven to 375°F. Dip each corn tortilla in warm birria consommé, then fry briefly in a hot skillet with reserved fat for 10-15 seconds per side until pliable.
08 - Fill each tortilla with shredded birria and a sprinkle of cheese. Roll tightly and place seam-side down in a baking dish.
09 - Pour remaining birria consommé over enchiladas. Top with remaining cheese. Bake for 10-15 minutes until cheese is melted and bubbly.
10 - Serve hot, generously garnished with diced white onion, chopped fresh cilantro, and lime wedges. Offer extra consommé on the side for dipping.