Place ½ C. Sugar and ½ C. water in a small saucepan. Bring to a boil over high heat. Reduce to medium heat and let simmer for 1 minute. Remove from heat and allow to cool for about 20 minutes.
When the syrup is no longer hot, place it in a blender or food processor with the fresh basil leaves and puree for 1-2 minutes, scraping down the sides with a rubber spatula, if needed. Mixture should be bright green and smooth, no chunks of basil should remain. Place basil syrup in a airtight container and refrigerate.
For the Blackberry Syrup:
Place the blackberries, 1 C. Sugar, and 1 C. water in a saucepan and bring to a boil over high heat. Reduce the heat to medium and simmer for 10 minutes, stirring occasionally.
Place the mixture in a blender or food processor and puree until smooth. Put the puree through a small mesh sieve, and discard the seeds. Refrigerate the remaining puree in an airtight container.
For the Lemonade Base:
Place the lemon juice, 1 C. Sugar, and 1 C. water in a saucepan and bring just to a boil. Remove from heat and place in an airtight container. Refrigerate.
To make the Frozen Lemonades:
Place about 14 ice cubes in a blender. Add ¼ C. lemonade base, ¼ C. water. and ⅓ C. blackberry puree to the blender and blend together until the ice becomes very fine and smooth. You'll want to check the taste of the lemonade and add more lemonade base, water, or blackberry puree as you see fit.
To serve, scoop about ¼ C. of the frozen lemonade into a glass and drizzle about 1 T. of the basil syrup over the top. Fill the rest of the glass up with the frozen lemonade. Garnish with blackberries and basil, if desired.
Recipe by The Kitchen McCabe at https://www.thekitchenmccabe.com/2014/06/03/frozen-blackberry-basil-lemonade/