In a medium bowl, combine the shredded chicken and barbecue sauce, tossing until the chicken is evenly coated.
Place a large non-stick skillet or griddle over medium heat and melt a small amount of butter.
Lay one tortilla flat and distribute 1/4 cup of the cheese blend over one half of the surface.
Layer 1/2 cup of the BBQ chicken mixture, 1 tablespoon of red onion, and 1/2 tablespoon of cilantro over the cheese.
Top with another 1/4 cup of cheese and fold the tortilla over the filling to create a half-moon shape.
Place the folded tortilla in the skillet and cook for 2 to 3 minutes until the bottom is golden brown.
Carefully flip the quesadilla and cook for an additional 2 minutes until the cheese is fully melted and the second side is crisp.
Repeat the process for the remaining ingredients.
Allow the quesadillas to rest for 1 minute before slicing into wedges for service.