Preheat oven to 250ºF. Wrap tortillas in a damp kitchen towel and cook in the microwave for a minute.
Lay the warm, pliable tortillas out on a clean, flat, work surface. Spread one tablespoon of jelly over each tortilla. Sprinkle a small handful of cheese over on half of the tortilla and top that with an even layer of sliced apples. Top the apples with more cheese and fold the quesadillas in half to create half moons.
In a skillet over medium to medium-high heat, drizzle some EVOO. Place the quesadillas one at a time in the hot pan and heat them on both sides until they are crispy and golden brown, and the cheese has melted, about 1-2 minutes per side. Transfer each cooked quesadilla to a baking tray in the oven to keep warm as you finish the others.