How to Make It
In a large bowl, toss the tomatoes with the cherries, Italian pepper, bread, red onion, vinegar, garlic, 1/2 cup of the olive oil and a very generous pinch each of salt and pepper. Let the gazpacho base stand at room temperature for 2 hours.
In batches, puree the gazpacho base until very smooth, about 2 minutes. Transfer to another large bowl. Cover and refrigerate for at least 3 hours or overnight.
Meanwhile, in a small saucepan of simmering water, blanch the basil until tender, about 1 minute. Drain well and cool under running water. Squeeze out the excess moisture and transfer to a blender. With the machine on, gradually add the remaining 1/3 cup of olive oil until the mixture is bright green and very smooth. Strain through a fine sieve into a small bowl, then season the basil oil with salt.
Season the gazpacho with salt, adding tablespoons of water if too thick. To serve, spoon the soup into bowls and garnish with slivered anchovy fillets, chopped pistachios, grated frozen goat cheese and the basil oil.