Combine peaches and maple syrup in a small saucepan over low heat. Grate ginger directly over peaches. Stir gently to mix.
Allow to cook on low for 20-30 minutes or until peaches are very soft and liquid begins to reduce.
You can break down the peaches with a potato masher or fork if you prefer that consistency but it is not necessary.
Serve warm or cooled. Store remainder in the refrigerator.