1. Blend the cheese and heavy cream together and set aside.
2. Cut cherry tomatoes in half and place into a mixing bowl.
3. Cut plum tomatoes in half and place in a second bowl. Divide the chicken broth, vinegar and olive oil between the two bowls. Add a pinch of sugar and season both bowl with salt and pepper. Sugar is added as a means to counteract the acidity of the tomatoes.
4. Puree the tomatoes, one color at a time, in a food processor.
5. To serve, ladle each soup into bowls equally, balancing the two colors. Serve chilled or at room temperature.