How to Make It
In a medium saucepan, combine the tomatoes with the olive oil, basil, garlic, vinegar and sugar. Season with salt and pepper. Cook over low heat until hot but not boiling, about 10 minutes. Pass the soup through the fine disk of a food mill into a medium bowl to remove the tomato seeds and skin. Chill the soup in the refrigerator or quick-chill it by setting the bowl in a larger bowl of ice water.
Using a small melon baller, scoop a total of 20 balls from the cucumber and melons. Alternatively, cut the cucumber and melons into 1/2-inch dice. Pour the soup into bowls. Garnish with the melon and cucumber balls and the basil sprigs and serve.
In winter, when most tomatoes are not very flavorful, plum tomatoes will still be good in this recipe.