Making Birria Quesadillas is straightforward if you follow these steps:

1. Prepare the Meat: In a large pot, add the beef or goat meat and cover it with water. Bring to a boil, then reduce heat and simmer until tender, about 1.5 hours.
2. Soak the Chilies: While the meat cooks, remove the stems and seeds from the guajillo and ancho chilies. Soak them in hot water for 15 minutes until softened.
3. Make the Sauce: In a blender, combine the soaked chilies, quartered onion, garlic, cumin seeds, oregano, black peppercorns, and a cup of beef broth. Blend until smooth.
4. Combine Meat and Sauce: Once the meat is tender, drain it and shred it with two forks. Add the shredded meat back to the pot, then pour in the chili sauce. Stir to combine and let it simmer for an additional 15 minutes.
5. Prepare the Tortillas: Heat a skillet over medium heat. Place a tortilla in the skillet and sprinkle with a generous amount of cheese.
6. Add the Filling: Spoon a portion of the birria mixture onto half of the cheese-covered tortilla. Fold the tortilla over to create a half-moon shape.
7. Cook the Quesadilla: Cook for 3-4 minutes on each side until the tortilla is golden brown and the cheese is melted. Repeat with remaining tortillas and filling.
8. Serve: Remove from skillet and slice into wedges. Garnish with chopped cilantro and serve with lime wedges and salsa.