Preheat the barbecue to high heat and oil the grate. Season the chicken thighs with salt and pepper, then grill for about 4 minutes on each side, or until the chicken is well done. Cool slightly, then dice and transfer to a bowl. Add a few spoonfuls of barbecue sauce and mix to coat the meat. Reserve.
For the Grilled Vegetables
Place the chopped vegetables on a plate and drizzle with some extra-virgin olive oil. Rub the oil all over the vegetables, then season with sea salt and black pepper. Preheat the barbecue to high heat and oil the grate. Grill for 6 to 8 minutes, turning the vegetables midway through. The vegetables are done when they’re tender but not soft. Cool slightly, then slice the vegetables thinly.
To Assemble the Quesadillas
Set a tortilla over a work surface. Over half of the tortilla, place two half slices of Monterey Jack cheese, then add a quarter of the barbecued chicken, grilled vegetables, and beans, then top with some fresh coriander. Finish with two more half slices of Monterey Jack cheese, then fold the tortilla in half. Gently press it down with your hand. Repeat the steps to assemble all quesadillas.
To Grill the Quesadillas
Preheat the barbecue to medium-high heat and oil the grate. Using a spatula, carefully transfer the folded quesadillas to the grill and cook for 3 to 4 minutes on each side, or until the tortillas are crispy and the cheese is melted. Cut the grilled quesadillas in slices and serve immediately with additional barbecue sauce and guacamole.
