In a medium bowl, combine the shredded chicken with BBQ sauce, honey, and hot sauce. Stir well until every piece of chicken is evenly coated in the glossy sauce. Set aside.

Heat olive oil in a skillet over medium heat. Add the sliced red onions and chopped bell peppers. Saute for about 5 minutes, stirring occasionally, until softened and lightly golden. Season with salt and pepper. Remove from heat.

Lay one flour tortilla flat on a clean work surface. Sprinkle an even layer of cheddar and mozzarella over one half of the tortilla. Spoon a generous layer of the BBQ chicken mixture on top, then add the sauteed vegetables. Finish with a scatter of fresh cilantro.

Fold the tortilla in half over the filling, pressing gently to seal.

Heat a clean skillet or griddle over medium heat. Place the filled quesadilla onto the surface and cook for about 3 minutes per side, pressing lightly with a spatula, until the tortilla is deep golden brown and the cheese is fully melted. Avoid high heat to prevent burning before the cheese melts.

Transfer to a cutting board and rest for 2 minutes before slicing into wedges. Repeat with remaining tortillas and filling.

Serve warm with sour cream and guacamole on the side if desired.