In a blender or food processor, combine the chopped tomatoes, cucumber, bell pepper, red onion, and garlic. Blend until smooth.
Add the tomato juice, olive oil, red wine vinegar, salt, black pepper, and cayenne pepper (if using) to the blender. Blend again until well combined.
Taste and adjust seasoning if necessary. If the mixture is too thick, add a little more tomato juice to reach your desired consistency.
Transfer the gazpacho to a large bowl or pitcher and refrigerate for at least 2 hours to chill and allow the flavors to meld.
Serve the gazpacho cold, garnished with fresh basil or parsley.