Remove stems and seeds from the dried chiles. Soak the chiles in hot water for 10 minutes until soft.
In a blender, combine the soaked chiles, onion, garlic, tomatoes, cumin, oregano, thyme, salt, and pepper. Blend until smooth.
In a large pot, brown the beef chunks over medium heat. Add the chile sauce, cinnamon stick, bay leaves, and enough water to cover the beef.
Bring to a boil, then reduce to a simmer. Cover and cook for 2-3 hours until the beef is tender and easily shredded.
Assemble the Quesadillas:
Heat a skillet over medium heat. Place a tortilla in the skillet, sprinkle with shredded cheese, and add a layer of shredded birria beef. Top with another tortilla.
Cook until the bottom tortilla is golden and the cheese begins to melt. Flip and cook the other side until golden and the cheese is fully melted.
Serve:
Cut the quesadillas into wedges. Garnish with fresh cilantro and serve with lime wedges.
This recipe not only combines traditional Mexican flavors with a modern twist but also aligns with the current food trends of exploring complex, rich flavors and fusion cuisine (Taste of Home) (The Wicked Noodle). Enjoy your delicious Birria Quesadillas!
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