Coat a large skillet or griddle with cooking spray and set pan over medium heat to preheat.
Using a fork, pull chicken meat from bone in shreds.
Arrange tortillas on a flat surface. Top one side of each tortilla with an equal amount of chicken, mushrooms and tomatoes. Top filling with shredded cheese (1/3 cup per tortilla). Fold over tortillas to cover filling, making half-moon shapes. Place quesadillas in (or on) prepared pan and cook 3 minutes per side, until tortillas are golden brown and cheese melts. Garnish with cilantro.