Peach Champagne Sorbet

I tried this recipe for the first time yesterday, and although I made a few mistakes, it turned out so nicely that I had to post the recipe for anyone else who may be interested.

A few words of warning:

1. Bite the bullet and spend more than ten dollars on the Champagne. It can make quite a bit of difference.
2. You can get much more juice out of a ripe peach, so make sure you select a slightly squishy one at the store.
3. Start this recipe when you know you'll be home and awake for a four hour stretch, since you need to stir the freezing sorbet periodically.

2 cups water
2 cups superfine sugar
1 fresh ripe peach, pitted and skinned
1 1/2 cups cold Champagne
Peach slices, for garnish (optional)

Mash peach pieces in a bowl until completely crushed or puree in a blender. Run the peach juice through a fine mesh strainer and reserve the liquid.
In a medium-sized pot, bring the water close to a boil, and then add the sugar, stirring until the sugar is completely dissolved. Bring the syrup to a slight boil. Add the peach juice, and then the Champagne (Warning: the Champagne will foam excessively when added to the pot, so pour slowly).
Immediately transfer the liquid to a large, non-reactive, freezer-safe bowl and place in the freezer. Freeze until ice crystals begin to form on the edges of the liquid. Using a whisk, thoroughly whip the mixture to break up all the ice crystals. Place back in the freezer. Whisk the sorbet every 30 minutes until it obtains the smooth texture and appearance of sorbet.
Serve in sorbet glasses with fresh peach slices.