Working in batches, combine the tomatoes, peppers, cucumber, onion (if using), garlic, olive oil, sugar, vinegar and bread in a blender or food processor. Blend until very smooth.
Strain into a bowl using a fine mesh strainer, pressing to extract as much liquid and pulp as possible. Stir in ice water to your desired consistency and add salt and black pepper to taste. Adjust vinegar level as needed.
Refrigerate for three hours or preferably overnight. Serve in small bowls with diced red and green pepper garnish.