Step 1: Prepare the Chiles. Remove stems and seeds from ancho, guajillo, and chile de arbol. In a dry skillet over medium heat, toast the chiles for 2-3 minutes, pressing them down occasionally, until fragrant. Be careful not to burn them.
Step 2: Rehydrate Chiles. Place toasted chiles in a heatproof bowl. Pour enough boiling water over them to cover. Let them rehydrate for 20-30 minutes until soft.
Step 3: Sear the Beef. Pat the chuck roast dry and season generously with salt and pepper. Heat 1 tablespoon of olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Sear the beef on all sides until deeply browned. Remove the beef and set aside.
Step 4: Sauté Aromatics. Add the remaining 1 tablespoon of olive oil to the same pot. Add chopped onion and minced garlic. Sauté until softened and fragrant, about 5-7 minutes.
Step 5: Blend the Adobo. Drain the rehydrated chiles (reserve about 1 cup of the soaking liquid). In a blender, combine the softened chiles, sautéed onion and garlic, diced tomatoes (undrained), apple cider vinegar, ground cumin, Mexican oregano, bay leaves, and whole cloves. Add 1 cup of the reserved chile soaking liquid. Blend until completely smooth. Add more soaking liquid if needed to achieve a thick, pourable sauce.
Step 6: Braise the Beef. Return the seared beef to the Dutch oven. Pour the blended adobo sauce over the beef. Add enough beef broth to almost cover the meat. Bring the mixture to a simmer, then reduce heat to low, cover, and braise for 3-4 hours, or until the beef is fork-tender.
Step 7: Shred the Beef and Prepare Consommé. Carefully remove the beef from the pot and place it on a cutting board. Shred the beef using two forks. Strain the braising liquid (consommé) through a fine-mesh sieve into a separate bowl, pressing on the solids to extract all liquid. Discard the solids. Skim off any excess fat from the consommé, reserving a small amount if desired for dipping tortillas. Return the shredded beef to a small amount of the strained consommé to keep it moist and warm.
Step 8: Assemble the Birria Tacos. Heat a large cast-iron skillet or griddle over medium-high heat. Dip a corn tortilla into the consommé (ensure both sides are coated). Place the tortilla on the hot griddle. Sprinkle with shredded Monterey Jack cheese and a generous amount of shredded birria beef.
Step 9: Cook the Tacos. Once the cheese starts to melt, fold the tortilla over and cook until crispy and golden brown on both sides. Repeat with remaining tortillas and filling to create more Birria Tacos.
Step 10: Serve. Serve your Birria Tacos hot with small bowls of the consommé for dipping. Garnish with chopped white onion, fresh cilantro, and a squeeze of lime juice. Enjoy!