Chop ¼ cup each of tomatoes, cucumber and bell pepper from the larger pieces. Place in a small bowl; cover and set aside in the refrigerator.
Working in two batches, puree the remaining tomatoes, cucumber and bell pepper with garlic, 3 tablespoons oil, 2 tablespoons vinegar, 1 teaspoon salt and ½ teaspoon pepper in a blender until smooth. Transfer to a large bowl, cover and refrigerate until chilled, at least 2 hours or up to 2 days.
Just before serving, chop avocado and add it to the reserved chopped vegetables. Stir in basil and the remaining 2 teaspoons oil, 1 teaspoon vinegar and pinch each of salt and pepper. Ladle the gazpacho into bowls and top with the chopped vegetable salad.
