01 - Heat olive oil in a large pot over medium heat. Add the chopped onion and sauté until translucent, approximately 5 minutes.
02 - Add minced garlic and cook until fragrant, about 1 minute.
03 - Incorporate the chopped or canned tomatoes with their juices along with tomato paste. Cook for 5 to 7 minutes to allow tomatoes to break down.
04 - Pour in vegetable broth and bring mixture to a boil. Reduce heat and simmer uncovered for 15 minutes, stirring occasionally.
05 - Stir in sugar (if using), salt, pepper, and fresh basil leaves. Continue simmering for an additional 5 minutes.
06 - Remove from heat and purée soup until smooth using an immersion blender or a countertop blender in batches.
07 - Return puréed soup to low heat. Stir in heavy cream and warm gently for 2 to 3 minutes, avoiding boiling.
08 - Taste and adjust salt and pepper as needed. Ladle into serving bowls, garnish with extra basil leaves and a drizzle of cream.