In a small bowl, combine sugar, ground ginger, cinnamon and fresh ginger. With clean hands, work the ginger into the sugar until well coated. The mixture should be sticky and fragrant. Set this spiced sugar mixture aside.
Add the peaches to a small saucepan with the spiced sugar mixture and water. Cook on low heat until the sugar has melted and the mixture begins to bubble. Stir often with a silicone spatula to keep the peaches from sticking to the bottom of the pan.
Turn off the heat. Add the champagne or other liquid. Stir in the butter and salt. Return to low heat. Cook on low, partially covered, for 20-30 minutes until peaches are softened but not jammy.
Remove from heat. Spoon warm onto cakes, pavlova or ice cream. Chill in the fridge in an airtight container up to five days.