Remove stems and seeds from guajillo, ancho, and chile de árbol chiles. Heat a dry skillet over medium heat and toast chiles for 30 to 45 seconds per side until fragrant and slightly darker. Transfer to a medium pot, cover with about 4 cups water, bring to a boil, then turn off heat, cover, and soak for 15 to 20 minutes until softened.
While chiles soak, halve the onion and char one half with tomatoes and garlic in a dry skillet over medium high heat for 8 to 10 minutes until blistered and blackened in spots. Drain softened chiles, reserving 1 cup soaking liquid. Blend chiles, charred vegetables, cinnamon stick, cumin seeds, oregano, cloves, apple cider vinegar, and 1 cup soaking liquid on high until smooth. Strain through a fine mesh strainer, pressing on solids.
Pat beef chuck and short ribs dry and season generously with salt and pepper. Heat neutral oil in a Dutch oven over medium high heat until shimmering. Working in batches, sear beef on all sides until deeply browned, about 3 to 4 minutes per side. Transfer to a plate and set aside.
Preheat oven to 325°F. Return seared beef to Dutch oven and pour strained chile sauce over top, stirring to coat. Add beef broth, remaining onion half, and bay leaves, then stir to combine. Bring to a gentle simmer on stovetop, cover with lid, transfer to oven, and braise for 2 1/2 to 3 hours until beef is fork tender and shreds easily.
Remove pot from oven and lift beef onto a cutting board, discarding bay leaves and onion half. Shred beef with two forks into bite sized pieces, discarding large pieces of fat or bone. Skim orange fat from top of braising liquid and set aside in a small bowl for frying. Taste remaining consomme and season with salt if needed. Ladle about 1 cup consomme over shredded meat and keep rest warm for serving.
Heat a comal or large skillet over medium heat and brush lightly with reserved fat. Dip a corn tortilla into warm consomme fat, coating both sides, then lay on hot comal. Sprinkle shredded Oaxaca cheese over half, add portion of shredded beef, fold into half moon shape, and press gently. Fry for 2 to 3 minutes per side until crispy and golden and cheese has fully melted. Repeat with remaining ingredients, keeping finished tacos warm.
Arrange crispy tacos on a platter alongside small bowls of warm consomme for each person. Top tacos with diced onion, chopped cilantro, and a squeeze of fresh lime just before eating. Dunk each bite into consomme and enjoy immediately while tortillas are still crispy.