Simmer the water and dissolve the sugar to form a simple syrup. Pour over the tomatoes and let cool.
Using a blender, puree the tomatoes, syrup and remaining ingredients until perfectly smooth. Taste for seasoning. Remember: The flavors will be slightly muted when this is chilled.
Place in your icecream maker and follow manufacturers instructions OR.
Pour into a non-reactive, freezer-safe dish and place in the freezer. Stir this mixture every hour until firm. The texture will depend on the tomatoes. Higher sugar content produces softer granita and less produces harder-icier granita.
Pull out of the freezer a few minutes before serving, to soften. Shave the granita ice with a fork or icecream scoop.