1. Toss together chopped tomatoes, the halved peaches, and the hyssop in a large bowl. Transfer tomato mixture to a food processor. Process mixture in batches until smooth. Transfer to a large nonreactive bowl. Stir in 1 1/2 tablespoons salt.

2. Drape a large piece of cheesecloth over another large bowl; pour tomato mixture onto cheesecloth. Gather corners of cheesecloth to enclose mixture, and tie corners around the handle of a long wooden spoon. Let bundle hang from the top shelf of the refrigerator over a large bowl so that liquid drips into bowl, at least 6 hours (or overnight). Discard solids in cheesecloth. Soup can be refrigerated in an airtight container up to 3 days, or frozen up to 1 month.

3. Divide the halved tomatoes and sliced peaches among serving bowls. Add 1 cup chilled soup to each bowl. Garnish with hyssop leaves and flowers. Sprinkle with salt.