Preheat a large non-stick skillet to medium-high heat. On a large cutting board, layer a tortilla with approx 1/4 cup of cheese, and then spread the vegetables out across it. Sprinkle an additional 1/4 cup or so of cheese on top.
Using a large spatula, transfer the quesadilla to the hot pan and let it cook for a couple minutes. When the cheese has begun to melt and the tortillas are browning slightly, turn the quesadilla over very carefully. Continue to cook until all the cheese is melted and the tortilla is crisp around the edges.
Using the spatula, transfer the quesadilla back to the cutting board, cut into triangles while it is hot and serve warm.