01 - Combine BBQ sauce, hot honey, smoked paprika, and garlic powder in a medium bowl. Add shredded chicken and toss until thoroughly coated in the sauce mixture.
02 - Arrange tortillas on a flat surface. On one half of each tortilla, layer mozzarella and cheddar cheese. Distribute BBQ chicken evenly among the tortillas, followed by diced red onion and cilantro if using. Top with remaining cheese. 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 2-3 minutes per side, pressing gently with a spatula, until tortilla is golden brown and cheese is fully melted. Repeat with remaining quesadillas, adding more butter as needed.
04 - Transfer cooked quesadillas to a cutting board and let rest for 1 minute to allow cheese to set. Slice each quesadilla into wedges.
05 - Serve warm with sour cream, fresh lime wedges, and additional hot sauce if desired.