How to Make It
In a blender or food processor, puree the chopped tomatoes until nearly smooth. Line a strainer with a double layer of cheesecloth and set over a medium bowl. Pour the tomato puree into the strainer and let drain in the refrigerator overnight. You should have about 1 cup of tomato water; reserve the solids for making soup or sauce. Whisk the honey and vinegar into the tomato water and season lightly with salt.
Pour the tomato water into an 8-inch-square glass or stainless steel baking pan. Freeze for 1 hour. Scrape the frozen edges into the center with a fork. Freeze for about 3 hours longer, scraping hourly, until the granita is uniformly icy and flaky.
In a large bowl, toss all of the tomatoes with the 3 tablespoons of olive oil and season with salt and pepper. Transfer to shallow bowls and spoon the granita on top. Garnish with chervil sprigs, drizzle with olive oil and serve.
Make the granita with blemished tomatoes, a.k.a. "seconds"—often overripe, they have the most flavor.