In a large, deep frying pan, heat 1 tablespoon oil over medium high heat. Slowly cook and stir onion until translucent. Mix in honey. Stir until onion is golden brown, about 5 minutes. Remove from pan and set aside.
Place remaining oil and chicken in the pan over medium high heat. Cook until chicken is no longer pink. Stir in barbecue sauce and evenly coat chicken.
Layer 4 tortillas individually with chicken, onions and Cheddar. Top with remaining tortillas.
One or two at a time, place layered tortillas on a large baking tray. Bake uncovered in the preheated oven 20 minutes, or until cheese is melted. Do not let tortillas become too crisp. Remove from heat. Cut into quarters to serve.