Cut bell pepper, cucumber, onion, and garlic into large pieces. Reserve 1/2 cup cucumber. Combine bell pepper, remaining cucumber, onion, and garlic in a food processor; process until finely chopped. Transfer mixture to a large bowl.
Cut tomatoes into large pieces. Reserve 1/2 cup tomato. Process remaining tomato in a food processor until finely chopped. Add to bell pepper mixture.
Stir in olive oil, vegetable juice, vinegar, and salt. Cover and chill 1 hour. Spoon into 6 bowls. Chop reserved cucumber and tomato. Top each serving with chopped cucumber, chopped tomato, and 1 tablespoon sour cream.
Note: Don't over process the vegetables; they need to be finely chopped, but not pureed.