Tomatoes should be served at room temperature, and this icy vinaigrette is a cool and resfreshing way to add contrast to the tomatoes.
To prepare granita, place the vinegar, oil, salt, and tomato in a blender or food processor and process until smooth. Place the tomato mixture in an 8-inch square baking dish, cover, and freeze until firm, stirring twice during the first 2 hours.
After about an hour, scrape with a fork and break up any big chunks. Scrape entire mixture with a fork until fluffy.
Arrange the tomato slices on a platter. Sprinkle the tomatoes with pepper and salt. Top with granita. Sprinkle with basil. Serve with bocconcini and Parmesean chunks drizzled with extra-virgin olive oil.