Step 1: In a medium bowl, combine the shredded cooked chicken with the BBQ sauce. Stir well until the chicken is evenly coated.
Step 2: Heat a large non-stick skillet or griddle over medium heat. Lightly brush one side of a tortilla with olive oil or butter.
Step 3: Place the oiled side down in the hot skillet. Sprinkle half of the tortilla with about 1/4 cup of shredded cheese, leaving the other half bare for folding.
Step 4: Spoon about 1/4 cup of the BBQ chicken mixture over the cheese on the filled half of the tortilla.
Step 5: Sprinkle a little more cheese (about 1-2 tablespoons) over the chicken mixture.
Step 6: Cook for 2-3 minutes, or until the cheese on the bottom half starts to melt and the tortilla is golden brown and slightly crispy. Carefully fold the bare half of the tortilla over the filled half, pressing down gently with a spatula.
Step 7: Continue to cook for another 2-3 minutes per side, pressing occasionally, until both sides are golden brown and crispy, and all the cheese is gooey and melted.
Step 8: Remove the cooked quesadilla from the skillet and place it on a cutting board. Let it rest for a minute or two before slicing into wedges.
Step 9: Repeat with the remaining tortillas and filling. Serve immediately with your favorite toppings like sour cream, guacamole, or salsa.