Pound chicken to even thickness, about 1/2 inch thick. Season chicken with some olive oil, chili powder, paprika, garlic powder, cumin, oregano, salt, and pepper. Let sit for 10 minutes.
Meanwhile season bell peppers and onion with some olive oil, salt, and pepper to taste.
Heat some olive oil on a large skillet over medium heat. Cook chicken, about 6-8 minutes per side, or internal temperature registers 165 degrees F. Transfer to a plate and set aside for 10 minutes. Cut into thin slices, and then cut each slice in half.
On the same skillet, cook the veggies about 8 minutes, or until cooked through, somewhat tender, and veggies have some charred spots. Transfer to a plate and set aside.
To assemble quesadillas: Heat 1/2 tablespoon of butter on a skillet on medium heat. On the skillet, lay a flour tortilla and then 1/2 cup cheese, followed by some chicken and cooked veggies, arranging evenly. Then top with another 1/2 cup cheese, and layer over another flour tortilla.
When the bottom tortilla is golden and bottom cheese has melted, flip the quesadilla and continue to cook on the second side until golden and cheese is melted. Repeat until you have 4 quesadillas.
Slice into 4 or 6 wedges per quesadilla. Serve immediately.