01 - Whisk together BBQ sauce, hot honey, smoked paprika, and garlic powder in a medium bowl until fully combined. Add shredded chicken and toss to coat evenly in the sauce mixture.
02 - Arrange tortillas on a flat surface. On one half of each tortilla, layer a portion of mozzarella and cheddar cheese. Distribute BBQ chicken evenly over the cheese, then top with diced red onion and cilantro if desired. Sprinkle remaining cheese on top, then fold tortillas in half to enclose filling.
03 - Melt 1/2 tablespoon butter in a large nonstick skillet over medium heat. Place one quesadilla in the pan and cook for 2 to 3 minutes per side, pressing gently with a spatula, until tortilla is golden brown and cheese is fully melted. Add more butter as needed and repeat with remaining quesadillas.
04 - Transfer cooked quesadillas to a cutting board and let rest for 1 minute. Slice each quesadilla into 3 to 4 wedges.
05 - Arrange quesadilla wedges on serving plates and accompany with sour cream, fresh lime wedges, and additional hot sauce for those who prefer extra heat.