Preheat a griddle or nonstick pan over medium heat. Place 1 tortilla on the griddle and when it starts to smoke, flip it over and top with 1/2 cup cheese. Sprinkle the chicken evenly over the cheese. Using a spoon, evenly spread the potatoes over the chicken. Top the potatoes with the red peppers and black beans, spreading evenly to the edges if possible. Continue by adding the artichoke hearts, broccoli, corn, olives, and carrots. Sprinkle the remaining 1/2 cup cheese, and top with the remaining tortilla.
Cook until the cheese is melted and bubbling, about 10 minutes. Then, using a spatula, quickly flip the quesadilla and cook another 5 minutes. Remove from the griddle. Cut in half and serve with desired toppings.