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 in the sauce mixture.
02 - Arrange tortillas on a clean work surface. On one half of each tortilla, layer mozzarella and cheddar cheese, followed by BBQ chicken mixture, diced red onion, and cilantro. Top with remaining cheese and fold tortilla in half to enclose filling.
03 - Melt 1/2 tablespoon butter in a large nonstick skillet over medium heat. Place folded quesadilla in pan and cook for 2–3 minutes per side, pressing gently with spatula, until tortilla turns golden brown and cheese melts completely. Repeat with remaining quesadillas, adding butter as needed.
04 - Transfer cooked quesadillas to a cutting board and let rest for 1 minute to allow cheese to set. Cut into wedges and serve immediately with optional sour cream, lime wedges, and additional hot sauce.