1. Prepare the Birria:

• Toast the Chiles: In a dry skillet over medium heat, toast guajillo and ancho chiles until fragrant, about 1-2 minutes. Soak them in hot water for 10 minutes to soften.
• Blend the Sauce: In a blender, combine softened chiles, chipotle pepper, onion, garlic, tomato paste, cumin, oregano, cinnamon, cloves, and 1 cup of beef broth. Blend until smooth.
• Sear the Meat: In a large pot or Dutch oven, heat vegetable oil over medium-high heat. Season the beef with salt and pepper, then sear on all sides until browned.
• Combine and Simmer: Pour the blended sauce over the meat, add the remaining beef broth and apple cider vinegar. Stir well. Bring to a boil, then reduce heat to low. Cover and simmer for 2.5 to 3 hours, until the meat is tender and shreds easily.
• Shred the Meat: Remove the meat from the pot and shred with forks. Reserve the cooking liquid as the consomé (dipping sauce).

2. Assemble the Quesadillas:

• Heat a Skillet: Preheat a skillet over medium heat. Lightly grease with oil or cooking spray.
• Dip and Fill: Dip one side of a tortilla into the consomé. Place it in the skillet, consomé side down. Add shredded birria meat and cheese on one half of the tortilla. Sprinkle with cilantro and diced onions if desired.
• Fold and Cook: Fold the tortilla in half. Cook until the cheese is melted and the tortilla is crispy, about 2-3 minutes per side.

3. Serve:

• Serve the birria quesadillas hot with a side of warm consomé for dipping and lime wedges on the side.