01 - Heat olive oil in a large saucepan over medium heat. Add onion and carrot, sauté for 5 minutes until softened.
02 - Add garlic and cook for 1 minute until fragrant.
03 - Add tomatoes with juices if using canned, vegetable broth, sugar, salt, and pepper. Bring to a boil, then reduce heat and simmer uncovered for 20 minutes, stirring occasionally.
04 - Remove from heat. Stir in basil leaves.
05 - Use an immersion blender or transfer to a blender in batches to puree the soup until smooth.
06 - Return soup to low heat. Stir in heavy cream and heat gently for 2–3 minutes. Adjust seasoning to taste.
07 - Ladle into bowls, garnish with extra basil, and serve hot.