1) Coat a large skillet or griddle with cooking spray. Set pan over medium heat to preheat. Using a fork, pull chicken meat from bone in shreds.
2) Arrange tortillas on a flat surface. Top one side of each tortilla with an equal amount of chicken, mushrooms, red peppers and artichokes. Top vegetables with grated cheese. Fold over tortillas, making a half moon.
3) Place quesadillas in (or on) prepared pan and cook for 3 minutes on each side, until golden brown and cheese melts.