Preheat oven to 425 degrees. Spray a large, nonstick skillet with the olive oil cooking spray. Preheat over medium high heat.
Add the mushrooms, garlic, and thyme to the skillet. Cook, stirring frequently, until the mushrooms release their juices and are browned. If the skillet begins to dry out periodically place the lid back on it to retain moisture.
Add the spinach to the skillet and cook, stirring frequently, for 1 to 2 minutes until the spinach is wilted. Remove the skillet from heat and set aside.
Lay the tortillas on a flat surface. Spread 1/8 of the mixture on the bottom half of each tortilla. Sprinkle each with a 1/4 cup of the cheese. Then, fold the top half of each tortilla over, enclosing the filling.
Spray 2 large baking sheeting with nonstick cooking spray.
Arrange the folded tortillas on the sheets and spray the tops lightly with the cooking spray. Bake for 5 minutes, flip the quesadillas with a spatula, and bake for 4 more minutes until lightly browned and the cheese is melted.