How to Make It
In a blender or food processor, puree the chopped tomatoes with a pinch each of salt and sugar. Line a strainer with 2 layers of cheesecloth and set the strainer over a medium bowl. Pour the tomato puree into the strainer, gather the ends of the cheesecloth and tie with a string. Let the tomato juices drain into the bowl for 2 hours. You should have about 1/2 cup of tomato water. If not, gently squeeze the cheesecloth to extract a little more of the tomato water. Whisk in 2 tablespoons of the olive oil and season the tomato water with salt and white pepper.
Rinse out the blender. Pour in the mozzarella liquidthere should be 3/4 cup. Cut each mozzarella ball into 6 pieces and add the pieces to the blender. Blend at low speed for 1 minute, then increase the speed to high and puree until smooth. Add the remaining 1/4 cup of olive oil and puree until creamy and smooth. Season the soup with white pepper.
In a medium bowl, toss the scallions and apricots with the lime juice and season with salt and pepper. Pour 1/2 cup of the mozzarella soup into each of 6 small bowls. Spoon the apricot mixture on top and garnish with the basil. Drizzle a few drops of the tomato water and the vin cotto on top and serve right away.
Look for imported Italian buffalo mozzarella, which comes packed in water in 500-gram plastic containers, at specialty markets and at cheese shops.