In a large pot over medium-high heat, sauté onion and carrots in oil until they are soft and translucent. Add tomato paste, garlic, and fresh basil and cook for 1-2 minutes.
Add tomatoes (do not drain) along with vegetable stock. Stir, and add granulated sugar and salt. Simmer gently over medium heat, uncovered, for 30 minutes.
Carefully ladle the soup mixture into a blender, making sure to allow air to escape out of the top so it doesn't explode as it blends. Holding a kitchen towel over the lid, blend until velvety and smooth.
Pour the soup back into the pot on low heat. Add butter, cream, and Balsamic Vinegar. Stir until well combined, and then taste for balance of seasonings. Add additional salt, cream, or Balsamic Vinegar to taste. Keep on low until ready to serve.
Garnish with additional cream, Balsamic, and basil if desired, and serve with torn pieces of warm, buttery, crusty bread or grilled cheese sandwiches.