Place the sugar and 1 1/2 cups water in a small saucepan and simmer until the sugar dissolves. Set aside.
Fill a large saucepan with water and bring it to a boil. Add the peaches and cook for between 15 seconds and 3 minutes, just until the skins peel off easily. (Ripe peaches will be ready sooner.) Transfer the peaches to a bowl of cool water, peel and cut in wedges into the bowl of a food processor fitted with the steel blade, discarding the pits. Puree the peaches completely and pour into a 9-by-13-inch baking dish.
Whisk the sugar syrup, Grand Marnier and vanilla seeds into the peach puree. Place the dish uncovered on a level shelf in the freezer for 30 minutes to 1 hour, until it begins to crystallize around the edges. Scrape the entire mixture, including the edges, with the tines of a fork and freeze for another 30 minutes. Continue freezing and scraping every 30 minutes, until the mixture is soft-frozen. It should take 2 to 3 hours to freeze and will be good to serve for up to 4 hours afterward. If the mixture gets too frozen, allow it to sit at room temperature for 30 minutes, and scrape it again with a dinner fork. Serve frozen in glasses.
The best way to ripen peaches is to place them in a brown paper bag with the top folded closed. Let them sit at room temperature for a day or two.