Preheat the Blackstone griddle over medium heat and lightly grease the surface with butter or oil.
In a bowl, combine the cooked chicken, BBQ sauce, hot honey, smoked paprika, garlic powder, salt, and pepper. Mix until the chicken is fully coated.
Place tortillas on the warm griddle and sprinkle cheddar and mozzarella cheese over one half of each tortilla.
Add the BBQ chicken mixture evenly over the cheese.
Top with sliced red onions and a little more cheese.
Fold the tortillas over to form quesadillas.
Cook for a few minutes on each side until the tortillas are crispy and golden brown and the cheese is fully melted.
Remove from the griddle and let them rest briefly before slicing.
Cut into wedges and drizzle with extra hot honey or BBQ sauce if desired.