Preheat grill to medium-high.
- Grill tomatoes and bell pepper, turning a few times, until they soften and the skins are blistered and charred in spots, about 8 minutes.
- Transfer the pepper to a plastic bag and let it steam until cool enough to handle. Peel off the skin; cut the pepper in half and discard the stem and seeds. Place one half in a blender.
- When the tomatoes are cool enough to handle, core and roughly chop. Add the tomatoes, skins and all, to the blender.
- Add half the cucumber to the blender along with bread, garlic, vinegar to taste, parsley, paprika or cayenne, salt and pepper.
- Blend until smooth. Add oil and blend until well combined.
- Refrigerate until room temperature or chilled, at least 1 hour.
- Before serving, finely dice the remaining cucumber and bell pepper; stir half of each into the gazpacho and garnish with the remaining cucumber and bell pepper.