For the peach compote: Combine peaches, water, and maple syrup in a small saucepan over medium-low heat. Grate ginger directly over peaches. Stir gently to mix. Allow to cook gently for 7 to 10 minutes or until peaches are very soft and liquid begins to reduce. Use an immersion blender to blend to desired consistency. (I like my chunky but you can also blend until smooth.) If you do not have an immersion blender, pour into any blender or food processor to puree.