Pour the tomato juice into a big saucepan and add the tomatoes. Simmer over medium heat for 30 minutes, stirring occasionally. Let cool a few minutes.
Carefully pour the hot tomato mixture into a blender and add the basil; blend until pureed.
Warm 1 cup of the heavy cream in a clean saucepan over very low heat. Gradually stir the pureed tomato mixture into the cream then stir in the butter. Warm the soup over medium-low heat until the butter melts, stirring often, without bringing it to a boil.
Season with salt and black pepper if you'd like, and swirl in a little more cream just before serving.