Cook red pepper, zucchini, yellow squash, onion, and mushrooms in olive oil in a large nonstick skillet over medium to medium-high heat until just tender, about 7 minutes. Transfer vegetables to a bowl.

Coat same skillet with cooking spray; place one tortilla in skillet. Sprinkle 1/4 cup cheese evenly over tortilla; layer 3/4 cup vegetable mixture on top. Sprinkle 1/8 cup more cheese on vegetables; top with a second tortilla. Cook until golden on both sides, about 2 to 3 minutes per side. Transfer quesadilla to a cutting board; cut into 8 triangles with a pizza cutter. Repeat with remaining ingredients. Serve hot.