In a large nonstick pan, cook red pepper, zucchini, yellow squash, onion, and mushrooms in olive oil over medium to medium-high heat for about 7 minutes, or until just tender. Remove vegetables from pan.
Coat the same pan with cooking spray, and place one tortilla in pan. Sprinkle 1/4 cup of cheese evenly over tortilla, and layer 3/4 cup of the vegetable mixture over the cheese. Sprinkle another 1/8 cup of cheese on the vegetables, and top with a second tortilla. Cook until golden on both sides, for approximately 2 to 3 minutes per side. Remove quesadilla from pan, and repeat with remaining ingredients. Cut each quesadilla into 8 triangles with a pizza cutter. Serve hot.