Preheat oven to 350 degrees. Place an oven safe skillet in the oven for 10 minutes until heated through.
While skillet is heating, chop chicken. Add 1 tablespoon of barbecue sauce to chicken and mix thoroughly. Set aside.
Add finely chopped basil to shredded cheese. Mix thoroughly and set aside.
Remove heated skillet from oven and set on a trivet. Lightly spray with cooking spray. Place 1 Mission Gluten Free Tortilla in skillet. Evenly sprinkle half of cheese on tortilla. Then spread chicken on top of cheese and remainder of cheese.
Take second tortilla and brush one side with remaining barbecue sauce. Place sauce side down on top of cheese layer. Place skillet back in oven for 5 minutes.
Remove skillet from oven. Carefully flip quesadilla. Place skillet back in oven and cook quesadilla for another 5 minutes until golden brown.
Remove skillet from oven. Cut quesadilla into four pieces. Serve with a side salad.