In a blender, combine the yogurt, basil, Lemon Simple Syrup, and ice. Blend until smooth and frothy. Pour into frosted glasses and serve immediately.
Lemon Simple Syrup:
In a small saucepan, combine the water, sugar, and lemon zest over medium heat. Bring to a boil, reduce the heat and simmer for 5 minutes, stirring occasionally, until the sugar has dissolved. Take the pan off the heat and allow the syrup to cool, about 20 minutes. Strain before using.