Pour the sugar, water, rum, lemon juice, brandy, and peach brandy into a large bowl over a large disk of ice. Stir until blended, and refrigerate for 1 hour. Add the peach slices to float, and serve in chilled glasses.
In this episode of CHOW Happy Hour, Martin Cate, of Smuggler's Cove in San Francisco, explains the culture of the Ti Punch from Martinique. If you order it on the Caribbean island, you might actually be in charge of making your cocktail yourself!