In a food processor or blender, puree the grapes and sugar until smooth. Pour into a small saucepan and bring to a boil over high heat. Reduce the heat to a simmer and cook until mixture has reduced by about one-third, about 15 minutes. Stir in the vodka, lemon juice, basil and salt, then let cool to room temperature.

Pour the mixture into a shallow pan and freeze until hard, 3 to 4 hours. Transfer to a food processor or blender and process until smooth and creamy and lightened in color. Serve immediately. Makes 2 cups.