Roughly chop the tomatoes and place them with the cucumber, bell pepper and peeled garlic in a blender. Blend until smooth. Add the sherry vinegar, two tablespoons of olive oil, salt and pepper and blend a little more until the soup emulsifies slightly and becomes creamier in color.
Chill the gazpacho for at least an hour. Chilled it tastes sharper and fresher; at room temperature it tastes flat. Taste again after chilling and adjust with salt or a few drops of vinegar.
Pour the soup into a deep bowl and place the burrata in the center. Tear it open so the creamy center melts into the soup. Drizzle the remaining olive oil over it and finish with basil and black pepper. The burrata provides the protein and fats that make this vegetable soup a complete lunch.