Heat a griddle to low heat. Melt half of the butter on the griddle, and place the tortillas in the hot butter. Cover each tortilla with 3 tablespoons of cheese, some of the chicken, and some of the BBQ sauce. Then add the rest of the cheese and fold the tortilla in half to cover the ingredients.
Continue to cook on low for a couple minutes on each side until the tortillas are crispy and the cheese is melty. Add salsa of your choice, if desired.