Place in a medium baking dish. Pour 2 cups of the barbecue sauce over chicken and let marinate for 2 hours in the refrigerator. Remove from marinade, season with salt and pepper to taste and grill for 7 to 8 minutes on both sides or until tender and cooked through. Transfer chicken to a plate and let cool. Preheat oven to 450 degrees. When chicken is cool enough to handle, slice. Toss with the reserved 1 cup of bbq sauce. Place 8 tortillas on a flat surface and sprinkle with 2 tablespoons of each of the cheeses and onion slices. Top with some chicken. Stack another tortilla on top and repeat. Top with the remaining 8 tortillas. Brush the top of the tortillas with oil and sprinkle with the chili powder. Place tortillas on a lightly oiled baking sheet and bake for 5 to 7 minutes or until golden brown and cheese has melted.
For the Smoked Tomato Salsa: Mix all ingredients together and season with salt and pepper to taste.
For the Buttermilk Dressing: Mix all ingredients together and season with salt and pepper to taste.
To serve: Place 1 quesadilla on each plate and cut into quarters. Top with a dollop of salsa and drizzle with the buttermilk dressing.