Peel, core and quarter the apples. In a medium Dutch oven or large stainless steel saucepan, combine the apple chunks, water, maple syrup, cinnamon stick and nutmeg. Cover and bring the mixture to a simmer over medium heat. Continue simmering, stirring occasionally, until the apples are tender and falling apart, about 15 to 20 minutes.

Remove the pot from the heat. For chunky applesauce, use a potato masher or a wooden spoon to break it up to your desired consistency. Stir in the freshly squeezed orange juice. Serve the applesauce warm or chilled. Leftover applesauce will keep well in the refrigerator for about 1 week, or for months in the freezer.