Frozen Honeydew-Basil Margaritas

In a small saucepan, combine the sugar and 1/2 cup of water and bring to a boil, stirring to dissolve the sugar. Add the basil leaves and blanch just until wilted, about 20 seconds. Pour into a blender and let cool slightly, then puree until smooth. Refrigerate until cold. In a blender, combine the frozen melon with the tequila, lime juice and 6 tablespoons of the basil puree; puree until smooth. Divide among chilled glasses and garnish with basil sprigs.