Start by pitting 1 pound of the peaches and roughly chopping them. Tumble them into a small saucepan, pour over the water, and cover. Place over medium-low heat and bring to a simmer, stirring occasionally. Keep it at a simmer for about 10 minutes, at which point the peaches will have virtually melted.
Simmer for another 5 minutes uncovered before stirring in the sugar. The best way to know just how much is to taste the liquid—if the peaches are very sweet you’ll only need a spoonful or two; if they could use some help add a bit more. At the same time, if you feel the peachiness could be a little stronger reduce it for a few minutes more. Shut off the heat, stir in the peach brandy, and set aside to cool.
Once the peachy juice is cooled, strain it through a fine-mesh sieve, and then through the sieve again, this time lined with cheesecloth (to remove all the little bits of pulp). You should end up with about 1-1/2 cups of the juice.
Pour the juice into a pitcher along with the wine, vodka, and remaining 1/2 pound of peaches, which you’ve pitted and sliced. Stir, cover, and refrigerate for at least 6 hours, but up to 12.
Serve chilled. If you want, serve a little carbonated/soda water alongside to add some extra sparkle and effervescence.