Add all ingredients to a blender and blend until completely creamy and no chunks of basil are visible (if this is not possible in your blender you can strain out the basil pieces with a fine wire strainer/colander if you would like or you can leave the basil pieces in the mixture). 

Follow the instructions of your ice cream maker. You'll likely need to freeze the ice cream bowl overnight prior to making the ice cream. Pour the ice cream base into the ice cream maker and turn it on. Allow it to churn until very thick and ice cream maker begins to slow down. Transfer to a loaf pan or sealable container and freeze.