Place ice cubes in a cocktail shaker; add all ingredients, except star fruit. Cover and shake vigorously for 10 to 15 seconds or until a light frost develops on the outside of the cocktail shaker. Strain into two martini glasses. Garnish each with a slice of star fruit. Makes 2 (5-ounce) servings.
In a small saucepan, combine sugar and water. Cook and stir over medium heat until sugar dissolves. Transfer to a small bowl or a 1-cup glass measure. Cover and chill for 1 hour before using. Makes 3/4 cup.