Take boneless chicken breast, wrap in foil and place in a glass bake pan. Bake for 40 minutes. Shred chicken with two forks and add to barbecue sauce. Spray the tortillas with cooking spray to keep them from sticking to the pan and make them a little crispier. Coat only one side and place (coated side down) on a cutting board or waxed paper. Sprinkle 1/4 cup of cheese over half of each tortilla. Top with green chiles and barbecue sauce with chicken. Fold tortillas in half, pressing gently.
Preheat oven to 350. In a hot 10-inch skillet cook quesadillas, two at a time, over medium heat for 6 to 8 minutes or until golden brown, turning once. Place quesadillas on a baking sheet. Keep warm in preheated oven for up to 30 minutes. Repeat with remaining quesadillas. Cut each quesadilla into 3 wedges. Serve with salsa, sour cream, and green onion.
Bacon, Tomato, & Avocado Quesadillas: Prepare as above, except substitute cheese for cheddar; use 8 crisp-cooked and crumbled bacon slices, 2 small seeded and coarsely chopped tomatoes, and 1 seeded, peeled, and chopped avocado for the filling. Omit the green chiles, barbecue sauce with chicken, salsa, sour cream, and green onion.