Step 1: Pat the beef chuck roast dry with paper towels and season generously with salt and black pepper. In a large Dutch oven or heavy-bottomed pot, heat 2 tablespoons of olive oil over medium-high heat. Sear the beef on all sides until deeply browned. Remove the beef and set aside.
Step 2: In the same pot, add the chopped onion and sauté for 5-7 minutes until softened and translucent. Add the minced garlic and cook for another minute until fragrant.
Step 3: Prepare your chiles: Remove stems and seeds from dried Guajillo, Ancho, and Chile de Arbol chiles. Briefly toast them in a dry pan over medium heat for 30-60 seconds until fragrant (be careful not to burn). Transfer to a heatproof bowl and cover with boiling water. Let them rehydrate for 20-30 minutes until softened.
Step 4: Drain the rehydrated chiles, reserving about 1/2 cup of the soaking liquid. In a blender, combine the softened chiles, fire-roasted diced tomatoes (undrained), 4 cups beef broth, apple cider vinegar, ground cumin, dried Mexican oregano, ground cloves, and a pinch of salt. Blend until completely smooth. If too thick, add a little reserved chile soaking liquid. Strain the chile mixture through a fine-mesh sieve into the Dutch oven with the sautéed onions and garlic, pressing down on the solids to extract all liquid. Discard solids.
Step 5: Return the seared beef to the Dutch oven with the strained chile sauce. Add the bay leaves and enough extra beef broth to just barely cover the meat. Bring to a simmer, then reduce heat to low, cover, and cook for 3-4 hours, or until the beef is fork-tender.
Step 6: Once cooked, remove the beef from the pot and shred it using two forks. Skim any excess fat from the surface of the consommé (the liquid remaining in the pot). Season the consommé with salt to taste.
Step 7: Heat a large cast-iron skillet or griddle over medium heat. Dip one side of a Masienda corn tortilla into the birria consommé, ensuring it's coated in the rich red oil. Place the wet side down on the hot skillet.
Step 8: Immediately sprinkle a generous amount of shredded Oaxacan or Monterey Jack cheese over half of the tortilla. Add a spoonful or two of the shredded birria beef on top of the cheese. Cook for 2-3 minutes until the cheese begins to melt and the bottom of the tortilla is crispy and lightly browned.
Step 9: Fold the other half of the tortilla over the filling, creating a half-moon shape. Press down gently with a spatula. Continue to cook for another 1-2 minutes per side until both sides are golden brown and crispy and the cheese is fully melted. Repeat with the remaining tortillas and filling.
Step 10: Serve the Masienda Beef Birria Quesadillas immediately with small bowls of the warm consommé for dipping, alongside chopped white onion, fresh cilantro, and lime wedges. Enjoy!