How to Make It
Process heirloom tomatoes in a food processor 30 to 60 seconds or until pureed. Line a colander with 2 layers of cheesecloth; place colander over a large bowl. Pour tomato puree into cheesecloth. Tie ends of cheesecloth together. Chill 24 hours to allow puree to drain.
Remove bowl from refrigerator, and gently press cheesecloth using back of a spoon to extract remaining liquid. (Yield should be about 4 cups.) Cover and chill.
Preheat oven to 250°. Core medium tomatoes, removing stem ends. Cut tomatoes in half; place, cut sides up, on a lightly greased aluminum foil-lined baking sheet; sprinkle with 1 tablespoon olive oil, 1/4 teaspoon sea salt, and 1/4 teaspoon sugar. Bake 2 hours.
Place 1 roasted tomato half in each of 4 serving bowls. Top with squash and next 4 ingredients; sprinkle with thyme and 1/4 teaspoon salt. Add remaining 1/4 teaspoon salt to tomato water, and divide tomato water among bowls. Drizzle with remaining 1 tablespoon olive oil, and serve immediately.
Total time does not include 24 hours for chilling in step 1.