In a large Dutch oven or pot, heat a tablespoon of oil over medium-high heat. Sear the beef chuck pieces on all sides until browned. Remove beef and set aside.
Add the onion and garlic to the pot and sauté until softened, about 5 minutes. While the onion and garlic are cooking, briefly toast the dried guajillo and ancho chiles in a dry skillet over medium heat for about 1 minute per side, until fragrant.
Remove the toasted chiles from the skillet, place them in a bowl, and cover with hot water. Let them soak for about 20-30 minutes until softened. Drain the chiles, reserving some of the soaking liquid.
Transfer the softened chiles, oregano, cumin, cinnamon, cloves, apple cider vinegar, and about 1 cup of the beef broth to a blender. Blend until smooth. Add a little of the reserved chile soaking liquid if needed to help blend.
Pour the chile mixture into the Dutch oven with the sautéed onions and garlic. Stir well.
Return the seared beef to the pot. Add the remaining beef broth, salt, and pepper. The liquid should almost cover the meat. If not, add a little more broth or water.
Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 3-4 hours, or until the beef is very tender and easily shreds with a fork.
Once the beef is tender, remove it from the pot and shred it using two forks. Skim off any excess fat from the surface of the liquid in the pot.
Return the shredded beef to the pot and stir it into the flavorful consommé. Keep warm.
To assemble the tacos, dip each corn tortilla in the consommé until lightly coated. Place the tortilla in a lightly oiled skillet or on a griddle over medium-high heat. Cook for about 1 minute per side, until lightly crisped.
Fill each tortilla with a generous portion of the shredded birria meat. Top with chopped white onion, cilantro, and crumbled queso fresco.
Serve immediately with salsa roja and lime wedges on the side.
Notes
For an extra crispy taco, you can fry the consommé-dipped tortillas until golden brown and slightly crispy.