1. Bring sugar and 1 cup water to a boil in saucepan. Boil 1 minute. Add ginger, and remove from heat.
2. Purée tomatoes in food processor until liquefied. Stir into ginger syrup; chill.
3. Strain tomato mixture through fine-meshed sieve to remove seeds and skins. (You should have about 4 cups.)
4. Churn in ice cream maker according to manufacturer’s directions. Transfer to 1-quart container, and freeze.