Step 1: Pat dry the beef chuck roast thoroughly with paper towels and season generously with salt and black pepper on all sides.
Step 2: Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Sear the seasoned beef on all sides until deeply browned, about 3-4 minutes per side. Remove beef and set aside.
Step 3: Reduce heat to medium. Add sliced onion to the pot and sauté until softened and translucent, about 5 minutes. Add minced garlic, bay leaves, dried oregano, ground cumin, and cloves. Cook for another minute until fragrant, stirring constantly.
Step 4: Briefly toast the dried guajillo, ancho, and arbol chiles in a separate dry skillet over medium heat for 30 seconds per side until fragrant. Remove stems and seeds, then place chiles in a heatproof bowl and cover with hot water. Let rehydrate for 20-30 minutes until softened.
Step 5: Drain the rehydrated chiles, reserving about 1/2 cup of the soaking liquid. Blend the chiles with apple cider vinegar, a splash of the reserved chile soaking liquid, and a little beef broth until very smooth. Strain the sauce through a fine-mesh sieve into the Dutch oven, pressing firmly on the solids to extract all liquid. Discard the solids.
Step 6: Return the seared beef to the pot. Pour in the remaining beef broth, ensuring the beef is mostly submerged. Add a tablespoon of tomato paste. Bring the mixture to a gentle simmer, then reduce heat to low, cover tightly, and cook for 3-4 hours, or until the beef is incredibly fork-tender and easily falls apart.
Step 7: Once cooked, carefully remove the beef from the pot and shred it using two forks. Skim any excess fat from the surface of the consomé (the birria broth) and reserve it. Season the consomé to taste with additional salt if needed.
Step 8: Prepare your Masienda tortillas. If using masa harina, press fresh tortillas. Otherwise, have your Masienda corn tortillas ready.
Step 9: Heat a large griddle or cast-iron skillet over medium-high heat.
Step 10: Dip each side of a Masienda tortilla into the reserved fat from the birria consomé (or directly into the consomé itself if you don’t have enough fat). Place the dipped tortilla on the hot griddle.
Step 11: Immediately sprinkle a generous layer of shredded Oaxaca or Monterey Jack cheese on one half of the tortilla.
Step 12: Top the cheese with a good portion of the shredded birria beef.
Step 13: Fold the other half of the tortilla over the filling, creating a half-moon shape. Press down gently with a spatula.
Step 14: Cook for 2-3 minutes per side, or until the tortilla is golden brown and crispy, and the cheese is melted and bubbling. Repeat with the remaining tortillas and filling.
Step 15: Serve the hot Masienda Beef Birria Quesadillas immediately with small bowls of the warm birria consomé for dipping, and garnish generously with fresh cilantro and finely diced white onion. A squeeze of fresh lime juice is highly recommended!