01 - Heat olive oil in a large pot over medium heat. Add diced onion and carrot, sautéing for 5 minutes until vegetables are softened and fragrant.
02 - Stir in minced garlic and cook for 1 minute until aromatic, being careful not to burn.
03 - Add diced tomatoes with juices, chopped basil, vegetable broth, sugar, salt, black pepper, and red pepper flakes if desired. Stir thoroughly to incorporate all ingredients.
04 - Bring mixture to a gentle simmer, reduce heat to low, and cook uncovered for 20 minutes. Stir occasionally to prevent sticking and ensure even cooking.
05 - Remove pot from heat. Using an immersion blender, puree soup directly in pot until completely smooth and velvety. Alternatively, carefully transfer soup to a standard blender in batches.
06 - Stir heavy cream into pureed soup. Reheat gently over low heat for 2-3 minutes, stirring constantly. Taste and adjust seasoning with additional salt or pepper if needed.
07 - Ladle hot soup into individual bowls. Garnish with fresh basil leaves and serve immediately while steaming hot.