In a small saucepan, combine granulated sugar and water and whisk to dissolve the sugar.  Bring to a boil, then remove from heat, and stir again to make sure that all of the sugar has dissolved.  Set this simple syrup aside to cool slightly, then chill completely in the refrigerator.

In a large bowl, combine buttermilk, chilled simple syrup, vanilla seeds, lemon juice and lemon zest.

Pour into an ice cream maker and churn according to manufacturer’s instructions. Once churned, if you notice that the lemon zest is clumped together, break it apart with your finger tips and stir with a spatula to mix throughout the ice cream mixture.

Serve immediately for soft serve or chill for several hours to firm up before serving by the scoop.