In a saucepan, combine the juice of 5 lemons, 3/4 cup sugar, and 3/4 cup water. Bring the mixture to a gentle boil, stirring until the sugar dissolves completely.

Once boiling, remove from the heat and add 1/2 cup of fresh basil leaves and the zest of 2 lemons. Allow the mixture to steep for 45 minutes while off the heat, letting the flavors infuse.

Strain the mixture through a fine-mesh sieve, discarding the basil and lemon zest. Stir in 2 cups of cold water to dilute the base.

Pour the mixture into a shallow baking dish and place in the freezer for 1 hour.

While the base begins to freeze, hollow out 6 of the juiced lemon halves. Freeze the lemon cups to use as serving vessels later.

After the first hour of freezing, use a fork to scrape the partially frozen mixture into fluffy crystals. Repeat this scraping process every hour for 4 more hours to achieve an ideal granita-like texture.

Spoon the basil lemon ice into the frozen lemon halves and serve immediately for a visually striking presentation.