In a large, deep skillet, 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 skillet and set aside.
Place remaining oil and chicken in the skillet over medium high heat. Cook until chicken is no longer pink. Stir in barbeque sauce and evenly coat chicken.
Layer 4 tortillas individually with chicken, onions, Cheddar cheese and Monterey Jack cheese. Top with remaining tortillas.
One or two at a time, place layered tortillas on a large baking sheet. 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.