Peel, quarter and core the apples, then cut them into chunks. In a large saucepan, combine them with the maple syrup, cider and cinnamon stick and bring to a bubble. Lower the heat a bit and, stirring occasionally, let rapidly reduce into a thick topping while you make the waffles.
Meanwhile, heat a waffle iron to high. Combine the waffle mix with the eggs, melted butter, 1 1/2 cups milk and lots of freshly grated nutmeg (about 1/2 teaspoon). Stir in the cheese. If the mixture gets too thick, stir in a little more milk. If the waffle iron is nonstick, fill it with the batter and cook until crisp. If its not nonstick, spray with cooking spray or brush with more melted butter, then fill and cook the waffles. Top with the maple-apple sauce.