01 - Heat olive oil in a large pot over medium heat and sauté chopped onion until translucent, approximately 5 minutes.
02 - Add minced garlic and cook for 1 minute until fragrant.
03 - Stir in chopped fresh tomatoes 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 to a boil. Reduce heat and simmer uncovered for 15 minutes, stirring occasionally.
05 - Add sugar, salt, pepper, and basil leaves; continue simmering for another 5 minutes.
06 - Remove from heat and purée soup until smooth using an immersion blender or countertop blender in batches.
07 - Return puréed soup to low heat; stir in heavy cream and warm gently for 2 to 3 minutes without boiling.
08 - Taste and adjust seasoning as needed.
09 - Ladle soup into bowls and garnish with extra basil leaves and a swirl of cream.