01 - Heat a dry skillet over medium heat. Toast the dried guajillo, ancho, and pasilla chiles for 1 to 2 minutes until fragrant, stirring frequently. Transfer to a bowl, cover with hot water, and soak for 15 minutes until softened.
02 - In the same skillet, roast the quartered onion, garlic cloves, and halved Roma tomatoes until slightly charred, about 5 minutes. Set aside.
03 - Drain the soaked chiles and transfer to a blender. Add the roasted vegetables, apple cider vinegar, oregano, thyme, cumin seeds, peppercorns, cloves, and 1 cup of beef broth. Blend until completely smooth.
04 - Heat vegetable oil in a large Dutch oven over medium-high heat. Pat the beef chuck and short ribs dry, then sear on all sides until well browned, about 3 to 4 minutes per side.
05 - Pour the blended chile sauce over the browned beef. Add the remaining 3 cups of 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 is very tender and easily shreds.
06 - Remove the beef from the pot. Shred with two forks, discarding bones and excess fat. Skim excess fat from the birria consommé, reserving about 2 tablespoons for frying tortillas.
07 - Preheat oven to 375°F.
08 - Dip each corn tortilla in the warm birria consommé. Heat a skillet over medium-high heat with a small amount of reserved fat. Fry each dipped tortilla for 10 to 15 seconds per side until pliable.
09 - Fill each tortilla with shredded birria and a sprinkle of cheese. Roll up tightly and place seam-side down in a baking dish.
10 - Pour the remaining birria consommé over the enchiladas and top with the remaining cheese. Bake for 10 to 15 minutes until cheese is melted and bubbly.
11 - Serve hot, garnished with diced white onion, chopped fresh cilantro, and lime wedges on the side.