Melt the butter in a skillet over medium heat.
Add the apples, brown sugar, and cinnamon. Cook until apples soften and mixture thickens, about 5-7 minutes.
Spread the apple mixture on one half of each tortilla. Sprinkle cheese on top if using, then fold in half.
Heat a clean skillet over medium heat and lightly grease it.
Cook each quesadilla until golden brown on both sides, about 2-3 minutes per side.
Slice into wedges and serve warm—ideally with a scoop of ice cream or a drizzle of caramel sauce.