Prepare a lemon simple syrup with the water, sugar and 1½ tablespoons of the lemon zest by combining all three in a medium saucepan set over medium-low heat.
Cook mixture until the sugar is fully dissolved.
Remove from heat.
Once the simple syrup is ready, add the basil and salt.
Let the mixture steep for 30 minutes.
Strain the chilled mixture through a fine mesh strainer.
Move the mixture to a 9″x13″ shallow glass or nonreactive dish.
Chill in the freezer until edges are frozen, about 1 1/2 hours.
Remove from the freezer; scrape with a fork, pulling from the edges into center.
Return to the freezer.
Repeat process every 30 minutes until the mix is the texture of shaved ice, about 4 hours.
To serve: Add a thin slice of lemon and a leaf of fresh basil to each serving.