Puree the tomatoes in a food processor; stir in vinegar, salt, pepper and sugar.
Spoon granita into the center of serving dishes, drizzle dressing around the edges and arrange shrimp over the top. Sprinkle with parsley and serve immediately.
Recommended ingredient: If sweet white wine vinegar is not available, use 7 tablespoons white wine vinegar plus one tablespoon sugar.
Classic Granita Method:
Pour the granita mixture into a wide and shallow container, such as a stainless steel baking dish (the shallower the container, the quicker the granita will freeze).
Cover with a lid, foil or plastic wrap. Freeze the mixture 1 to 2 hours, until it is solid around the edges. Take the container out of the freezer and scrape the ice with a fork, mixing it from the edges into the center.
Repeat this scraping and mixing process every 30 minutes or so (at least three times) until the entire mixture has turned into small, sequined ice flakes. When ready to serve, "rake" with a fork to loosen the granita and spoon into serving dishes.
Quick Granita Method:
Note: This method is faster, but the granita will have a different texture—less icy and more slushy.
Pour the granita mixture into ice trays, cover with plastic wrap, and allow to freeze solid. Process the cubes in a food processor when you're ready to serve.