1. Heat the butter and olive oil in a large pot over medium heat.

2. Add the chopped onion and cook for 5 to 6 minutes until soft and translucent.

3. Stir in the minced garlic and cook for 30 seconds until fragrant.

4. Add the tomato paste and stir for 1 minute to deepen the flavor.

5. Pour in the whole peeled tomatoes with their juices and add the vegetable broth.

6. Stir in the sugar, salt, and black pepper, breaking up the tomatoes with a spoon.

7. Bring the soup to a gentle simmer and cook for 20 to 25 minutes.

8. Blend the soup until completely smooth using an immersion blender or carefully in batches with a standard blender.

9. Return the soup to low heat and stir in the heavy cream and fresh basil.

10. Taste and adjust seasoning if needed, then serve hot with crusty bread and an extra swirl of cream on top.