In a large skillet, melt 2 tablespoons of butter over medium heat. Add the chopped onion and green bell pepper, cooking until they are soft and translucent, about 5-7 minutes. Stir in the finely chopped chipotle peppers, crushed red pepper flakes, smoked paprika, and season with salt and pepper. Cook for another 2 minutes until the spices become fragrant.
Once the vegetables are ready, add the 2 cups of leftover shredded beef short ribs or brisket to the skillet. Stir everything together, allowing the beef to heat through and absorb the flavors of the spices. This should take about 3-4 minutes.
Lay out 4 of the flour tortillas on a clean surface. Evenly distribute the beef and vegetable mixture over each tortilla, topping with a generous amount of shredded Mexican cheese. Place the remaining tortillas on top to create quesadillas.
In the same skillet, melt another 2 tablespoons of butter over medium heat. Carefully place one quesadilla in the skillet and cook for about 3-4 minutes on each side, or until golden brown and the cheese is melted. Repeat this process for the remaining quesadillas, adding more butter as needed.
Once cooked, remove the quesadillas from the skillet and let them sit for a minute. Cut them into wedges and serve warm with your favorite toppings, such as guacamole, salsa, or sour cream.