01 - Heat olive oil in a large pot over medium heat. Add diced onion and chopped carrot, sauté for 5 to 6 minutes until softened.
02 - Stir in minced garlic and cook for 1 minute until fragrant.
03 - Add diced tomatoes with juice, vegetable broth, sugar, salt, black pepper, and optional red pepper flakes. Bring the mixture to a simmer.
04 - Reduce heat to low, cover, and let simmer for 20 minutes, stirring occasionally, until vegetables are very tender.
05 - Remove from heat and stir in chopped fresh basil leaves.
06 - Using an immersion blender or working in batches with a countertop blender, purée the soup until smooth and creamy.
07 - Return soup to low heat, stir in heavy cream, and warm gently without boiling. Adjust seasoning to taste.
08 - Ladle soup into bowls, garnish with additional fresh basil, and serve hot.