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, about 3-4 minutes per side. Remove the beef and set aside.
Step 2: Reduce the heat to medium. Add the chopped onion to the pot and sauté until softened and translucent, about 5 minutes. Add the minced garlic and cook for another minute until fragrant. Stir in the dried oregano, cumin, and bay leaves. Cook for 30 seconds until aromatic.
Step 3: While the aromatics cook, prepare your chiles. Remove the stems and seeds from the ancho, guajillo, and arbol chiles. Heat a dry skillet over medium heat and toast the chiles for 1-2 minutes per side until fragrant and slightly pliable (be careful not to burn them, as they will become bitter). Transfer the toasted chiles to a bowl and cover with boiling water. Let them rehydrate for 20-30 minutes until soft.
Step 4: Drain the rehydrated chiles, reserving a bit of the soaking liquid. Transfer the chiles to a blender along with the sautéed onion and garlic mixture, 1 cup of beef broth, apple cider vinegar, and a pinch of salt. Blend until very smooth, adding a little more chile soaking liquid or beef broth if needed to achieve a pourable consistency.
Step 5: Return the seared beef to the Dutch oven. Pour the chile sauce over the beef. Add the remaining beef broth (if not already used for blending) and enough water to almost cover the meat. Bring the mixture to a simmer, then reduce the heat to low, cover, and cook for 3-4 hours, or until the beef is fall-apart tender. Alternatively, you can cook it in a slow cooker on low for 6-8 hours or on high for 3-4 hours.
Step 6: Once the beef is cooked, carefully remove it from the pot and transfer it to a large bowl. Using two forks, shred the beef. Skim off any excess fat from the surface of the braising liquid (consommé) and reserve some for frying the quesadillas. Strain the consommé through a fine-mesh sieve into a separate pot, pressing on the solids to extract all liquid. Discard the solids. Season the shredded beef with some of the consommé to keep it moist and flavorful. Keep both the beef and consommé warm.
Step 7: In a large bowl, combine the Masienda masa harina with warm water and a pinch of salt. Mix with your hands until a soft, pliable dough forms. It should be moist but not sticky. If it's too dry, add a little more water; if too sticky, add a little more masa. Knead for a few minutes until smooth. Cover the dough with a damp cloth and let it rest for 10-15 minutes.
Step 8: Divide the masa dough into 1.5-inch balls (about 25-30g each). Place a ball between two pieces of plastic wrap in a tortilla press and press firmly to form a thin, even tortilla. Carefully peel off the plastic. If you don't have a tortilla press, you can use a rolling pin between two sheets of parchment paper.
Step 9: Heat a comal or heavy-bottomed skillet (cast iron works best) over medium-high heat. Cook each tortilla for about 45-60 seconds on the first side, then flip and cook for another 1-2 minutes. The tortilla should puff up slightly. Flip one more time and cook for another 30 seconds. Transfer cooked tortillas to a tortilla warmer or a plate covered with a clean kitchen towel to keep them warm and soft.
Step 10: Heat a large skillet or griddle over medium heat. Add a tablespoon or two of the reserved birria fat (from Step 6) to the hot skillet. If you don't have enough fat, use vegetable oil.
Step 11: Dip a fresh Masienda masa tortilla into the warm consommé, ensuring both sides are lightly coated. Place the dipped tortilla onto the hot skillet. Immediately sprinkle a generous amount of shredded cheese (Oaxaca or Monterey Jack work beautifully) over half of the tortilla.
Step 12: Pile a good spoonful of the shredded birria beef onto the cheese. Fold the other half of the tortilla over the filling to create a half-moon shape. Press down gently with a spatula.
Step 13: Cook for 2-3 minutes per side, until the tortilla is golden brown and crispy, and the cheese is melted and gooey. Repeat with the remaining tortillas, adding more birria fat to the skillet as needed.
Step 14: Serve the hot Masienda Beef Birria Quesadillas immediately with small bowls of the warm consommé for dipping. Garnish with chopped cilantro, diced white onion, and a squeeze of fresh lime juice.