1. Heat the coconut sugar and 1 cup water in a small saucepan over medium-high heat, stirring occasionally, until the sugar has dissolved. Remove from heat, add 6 sprigs of basil, cover, and let steep for 30 minutes. Strain into a pitcher, discarding the basil leaves. Stir in the lime juice and the remaining water; chill for 1 hour.
2. Add the frozen blueberries to the pitcher. Pour into ice-filled glasses, garnish with fresh basil leaves, and serve. Try a bubbly version by filling the glasses only halfway with the limeade and topping off with sparkling water.