Wash, peel, and roughly chop the tomatoes, cucumber, bell peppers, red onion, and garlic. Set aside a handful of diced cucumber, tomato, and peppers for garnish, if desired.
In a large blender or food processor, add the chopped tomatoes, cucumber, bell peppers, onion, and garlic. Drizzle in the olive oil and vinegar, then add salt, black pepper, and smoked paprika. Blend until smooth or leave slightly chunky for more texture, according to your preference.
Pour in the chilled tomato juice and blend again to combine. Taste and adjust seasoning as needed. If too thick, add more tomato juice or a splash of cold water.
Transfer the blended soup to a large bowl or pitcher, cover, and chill in the refrigerator for at least 2 hours to let the flavors meld (overnight is even better).
Stir well, then ladle gazpacho into chilled bowls or glasses. Top with reserved diced veggies, a drizzle of olive oil, and fresh basil or parsley. Serve cold and enjoy!