In a medium mixing bowl, combine the shredded chicken, BBQ sauce, and hot honey. Stir until the chicken is thoroughly and evenly coated.
Heat a large non-stick skillet or griddle over medium heat.
Spread approximately 1/2 tablespoon of butter onto one side of each flour tortilla.
Place one tortilla, buttered side down, into the preheated skillet.
Distribute 1/4 cup of cheese over one half of the tortilla. Layer 1/2 cup of the chicken mixture and 1 tablespoon of red onion over the cheese.
Top the filling with an additional 1/4 cup of cheese and fold the tortilla in half to cover the filling.
Cook for 2-3 minutes per side, pressing down lightly with a spatula, until the exterior is golden brown and the cheese is fully melted.
Transfer the quesadilla to a cutting board and allow to rest for 1 minute before slicing into thirds.
Garnish with chopped cilantro and serve immediately with extra hot honey if desired.