Roughly chop the tomatoes, cucumber, bell pepper, and onion.
Blend the Soup
In a blender or food processor, combine the tomatoes, cucumber, bell pepper, onion, garlic, olive oil, red wine vinegar, salt, and pepper. Blend until smooth or leave slightly chunky, depending on your preference.
Add Tomato Juice
Pour in the tomato juice and blend again until well combined.
Chill
Transfer the gazpacho to a large bowl or container. Cover and refrigerate for at least 2 hours to let the flavors meld.
Serve
Stir the soup before serving. Garnish with fresh basil or parsley, a drizzle of olive oil, and a sprinkle of smoked paprika if desired.