01 - Whisk together BBQ sauce, hot honey, smoked paprika, and garlic powder in a medium bowl until thoroughly combined. Add shredded chicken and toss to coat evenly.
02 - Arrange tortillas on a flat surface. On one half of each tortilla, layer mozzarella and cheddar cheeses. Distribute BBQ chicken mixture evenly, followed by diced red onion and cilantro. Top with remaining cheese. Fold tortillas in half.
03 - Melt 1/2 tablespoon butter in a large nonstick skillet over medium heat. Place one quesadilla in the pan and cook for 2-3 minutes per side, pressing gently with a spatula, until tortilla is golden brown and cheese is fully melted. Repeat with remaining quesadillas, adding butter as needed.
04 - Allow cooked quesadillas to rest for 1 minute before cutting into wedges. This prevents the cheese from immediately running out.
05 - Transfer quesadilla wedges to a serving platter. Accompany with sour cream, fresh lime wedges, and additional hot sauce for those who prefer extra heat.