01 - In a medium mixing bowl, whisk together BBQ sauce, hot honey, smoked paprika, and garlic powder until fully incorporated. Add the shredded chicken to the bowl and toss thoroughly until every piece is evenly coated with the sauce mixture.
02 - Lay out the flour tortillas on a flat surface. On one half of each tortilla, distribute an even layer of mozzarella and cheddar cheese blend. Top with equal portions of the sauced chicken, followed by diced red onion and fresh cilantro. Complete with a final sprinkling of remaining cheese, then fold the tortilla in half to enclose the filling.
03 - Melt 1/2 tablespoon butter in a large nonstick skillet over medium heat. Place one assembled quesadilla in the pan and cook for 2 to 3 minutes per side, pressing gently with a spatula, until the tortilla achieves a golden-brown crispness and the cheese is completely melted. Continue with remaining quesadillas, adding additional butter as necessary.
04 - Transfer cooked quesadillas to a cutting board and allow them to rest for 1 minute. This brief resting period helps the cheese set slightly, making for cleaner cuts. Slice each quesadilla into wedges.
05 - Arrange quesadilla wedges on serving plates and accompany with sour cream, fresh lime wedges, and additional hot sauce for guests who prefer extra heat.