Cut the bread into little cubes and fry them in half the olive oil. Set them on one side. Cut the half the tomatoes, onion, red pepper and cucumber into tiny dice, as small and neatly as possible. Chop the other half of the vegetables roughly and put them with all the other ingredients, except the basil, into a food processor. Pulse until smooth. Chill until you are ready to serve the soup.
At that point, whisk the soup to distribute the oil evenly. Serve it with the croûtons, the jewel-like diced vegetables and the chopped basil in small bowls, ready for each person to scatter into their soup.