Preheat oven to 425 degrees, with racks in upper and lower thirds. Lightly brush two rimmed baking sheets with oil, and place in oven to warm up.
In a small bowl, combine honey, mustard; set aside. Place 4 tortillas on a work surface, dividing evenly sprinkle with half the cheese, top with trukey, honey mixture, and apples,finish with remaining half of cheese. Cover with remaining 4 tortillias and brush tops with oil.
Carefully remove hot baking sheets from oven; place two quesadillas on each. Bake until golden, about 20 minutes flattening with a spatula, and rotation sheets halfway through. Let cool, cut like a pizza and serve.