In a large skillet over medium-high heat, add in the olive oil, and allow it to heat until it begins to swirl in the pan.
Toss in the black beans, corn, pepper, and onion and cook for 3 to 5 minutes, stirring occasionally until the vegetables are tender. Remove from the heat.
Place two tortillas on a clean work surface and lightly spray both tortillas with cooking spray, flip both tortillas over and top each tortilla with ½ of the vegan cheddar shreds (¼ cup on each tortilla) and then half of the veggie filling on each tortilla on top of the cheese.
Spread the mixture in an even layer and top with the remaining two tortillas and lightly spray with cooking spray.
Heat the large skillet over medium heat, add the quesadillas (you may have to cook them one at a time), and cook for 8 to 10 minutes or until the vegan cheese begins to melt and the tortillas are lightly browned, turning once.
Cut the quesadillas into wedges and serve immediately while still warm.