To make Lemongrass Simple Syrup: Combine sugar and water in a heavy small saucepan. Bring to a simmer over medium heat. Stir until the sugar is dissolved; add lemongrass pieces and simmer 3 to 5 minutes longer. Remove from the heat. When cool, cover and refrigerate for up to 2 weeks.

To make a cocktail: Place cold grapes and ginger in a shaker and muddle well. Add the ice, vodka, lemongrass syrup, and lime juice; shake well. Pour into glass over ice, and finish with frozen grapes and a lemongrass stalk.