In a large saucepan over high heat, add the simple syrup and coconut water and bring to a boil. Add the purple basil and boil for 2 minutes. Add the lime juice and stir. Remove from heat and pour mixture into blender. Blend on high for 2 minutes. Strain twice through a fine mesh sieve. Refrigerate for 1 hour. Makes enough basil cocktail mixture for 10 drinks.

When ready to serve, chill a martini glass. Fill shaker with ice, add the rums and 2 ounces of the basil cocktail mixture and shake vigorously. Strain the rum and basil mixture into glass. Garnish with a basil leaf.