Combine the shredded chicken and bbq sauce in a small bowl and warm up in microwave for 30 seconds to 1 minute, until heated through.
Meanwhile heat a non-stick pan or griddle over medium-high heat. Once hot, place the large tortillas down (you may have to do one at a time depending on the size of your griddle). Place ½ cup of cheese on one side of each of the tortillas, spreading out to reach the edges of the tortilla. Top each side of the tortillas with ½ of the shredded chicken, ½ of the purple onion and ½ of the cilantro. *if desired, drizzle a little bbq sauce on top.
Finish by using the remaining cheese and sprinkling it over the filling. Fold over the tortillas, enclosing the filling and let cook on one side until the tortilla is browned and the cheese is melty. Carefully flip over and finish cooking on other side until browned.
Remove quesadillas from griddle and slice into wedges. Enjoy!