Tomato Cucumber Gazpacho

Name: Tomato Cucumber Gazpacho
Ingredients: 5 cups coarsely chopped tomatoes (about 6 medium); 3 cups tomato-based vegetable juice; 2 1/4 cups chopped English hothouse cucumber (from 1 large), divided; 1 cup chopped red onion (about 1 small), divided; 1/4 cup extra-virgin olive oil; 2 tablespoons finely chopped fresh basil plus additional for garnish; 2 tablespoons plus 1 teaspoon red wine vinegar; 2 tablespoons mayonnaise; 3 small garlic cloves, peeled; 2 teaspoons anchovy paste; Purchased Parmesan croutons (optional; for garnish)