Rinse and halve the peppers, then remove the seeds and membranes. Peel and halve the cucumber lengthwise, and remove the seeds. Finely dice 1/4 of the peppers and cucumbers. Coarsely chop the rest. Peel and finely chop the red onion. Blanch the tomatoes in boiling water. Transfer to an ice water bath, then peel, quarter, and remove the seeds. Press through a fine strainer, collecting the juice in a bowl.
Peel and chop the onion and garlic. Remove the crust from the bread and soak in 4-5 tablespoons of lukewarm water. Add the coarsely diced vegetables, onions, garlic, tomato quarters, tomato juice, squeezed white bread, lemon juice, paprika, and olive oil to a blender. Puree completely. If the soup is too thick, thin with some water. Chill until ready to serve, at least 1 hour. Season to taste with salt and pepper. Garnish with the finely diced vegetables and diced red onion.