01 - Heat olive oil in a large saucepan over medium heat. Add the chopped onion and carrot if using, sauté until softened, about 5 minutes.
02 - Stir in minced garlic and cook for 1 minute until fragrant.
03 - Add canned tomatoes with juice, vegetable broth, sugar, oregano, salt, and pepper. Bring mixture to a gentle simmer.
04 - Cover and simmer for 20 minutes, stirring occasionally, until vegetables are very soft.
05 - Remove from heat and stir in fresh basil leaves.
06 - Using an immersion blender or working in batches with a countertop blender, puree soup until completely smooth and creamy.
07 - Return soup to low heat. Stir in heavy cream and warm gently for 2 to 3 minutes without boiling. Adjust seasoning to taste.
08 - Ladle into bowls, garnish with extra cream and basil leaves, and serve hot with crusty bread or croutons if desired.