In a medium bowl, combine the sliced apples, brown sugar, and ground cinnamon. Toss until the apples are evenly coated.
In a skillet over medium heat, melt the butter. Add the apple mixture and cook for about 5-7 minutes, stirring occasionally, until the apples are tender. Remove from heat.
Place one tortilla in the skillet over low heat. Sprinkle half of the shredded cheddar cheese evenly over the tortilla.
Spoon half of the cooked apple mixture over the cheese, and sprinkle with half of the walnuts if using. Top with another layer of cheese and place the second tortilla on top.
Cook for about 3-4 minutes until the bottom tortilla is golden brown and the cheese begins to melt. Carefully flip the quesadilla and cook for an additional 3-4 minutes until the other side is golden brown and the cheese is fully melted.
Remove from the skillet and let cool for a minute before slicing into wedges. Serve warm, drizzled with maple syrup if desired.