Add the water, sugar, lemon zest, and basil to a medium sauce pan. Over medium heat bring the mixture to a boil.
Once the mixture comes to a boil turn the heat down slightly and continue to simmer for 5 minutes. Remove from the heat after the 5 minutes and cover. Let this mixture steep for 15 minutes.
Strain the mixture into a bread pan and discard the lemon zest and basil leaves.
Add the lemon juice. Cool for about 10 minutes and set in the refrigerator.
Once the mixture is chilled move it to the freezer. After 30 minutes take a fork and scrape the ice off of the sides of the bread pan. Continue this process until the mixture is frozen.
Scoop into dessert dishes and serve.