Combine in a small saucepan:

Cook over medium heat, stirring, just until the sugar is dissolved. Let cool. Puree in a food processor or blender:

Strain through a fine-mesh sieve into a bowl; discard the seeds or skins. Stir the puree into the cooled syrup. Refrigerate until cold or quick-chill in an ice water bath.

Pour the granita base into a 13 × 9 × 2-inch baking dish. Place in the freezer. Every 30 minutes, scrape the mixture with a fork, stirring the frozen crystals from the edges of the dish back into the liquid, loosening and breaking up the crystals. Repeat until the mixture is completely frozen, about 3 hours.