For the soup:
Soak the bread, in a medium bowl of water to soften, about 15 to 20 minutes. Squeeze out the excess water and place in a large bowl. Coarsely chop the tomatoes, 2/3 of the cucumber, 1/2 the onion, and 1/2 the pepper and add to the bread. Add the garlic, season with salt, and drizzle with olive oil. Mix to combine and let sit for about 20 to 30 minutes to allow the flavors to marry and to let the salt pull some moisture out of the tomatoes.
Meanwhile, for the garnish, dice the remaining cucumber, onion and green pepper into perfect 1/4-inch dice and reserve.
Working in batches, puree the tomato/bread mixture in a blender with the vinegar. Blend in tomato juice to loosen the mixture, if needed. Remove soup to a large bowl and stir in about 1/2 cup of high quality olive oil. Taste for salt and add more, if needed.
Chill. Serve cold garnished with the diced cucumber, pepper and onion. Drizzle with a little more olive oil, if desired.