Bring a medium pot of water to a boil, then take one of the heirloom tomatoes and drop it in for 1 minute. When the time is up, place it immediately in a bowl of ice water for 30 seconds. Take out the tomato and the skin should easily rub off in your hand. Then slice it in quarters and scoop out the seeds.
Place vinegar, oil, 1/4 teaspoon salt, and the seeded peeled tomato in a blender or food processor; process until smooth. Place tomato mixture in an 8-inch square baking dish; cover and freeze until firm, stirring twice during first 2 hours. Remove mixture from freezer; scrape entire mixture with a fork until fluffy.
To prepare salad, arrange tomato slices on a platter. Sprinkle tomatoes with pepper and 1/4 teaspoon salt. Top with tomato puree. Sprinkle with basil.