01 - Heat olive oil in a large pot over medium heat. Add diced onion and carrot; sauté for 5 minutes until softened.
02 - Incorporate minced garlic and cook for 1 minute until fragrant.
03 - Stir in chopped tomatoes with their juices (or canned tomatoes), vegetable broth, water, sugar if using, salt, and black pepper. Bring mixture to a boil.
04 - Reduce heat to a low simmer and cook uncovered for 20 to 25 minutes, stirring occasionally, until tomatoes and vegetables are very soft.
05 - Remove pot from heat and stir in fresh basil leaves.
06 - Use an immersion blender to puree the soup until smooth or carefully blend in batches using a countertop blender.
07 - Return the pureed soup to the pot, stir in cream if desired, and gently reheat. Adjust seasoning to taste.
08 - Ladle into bowls and garnish with additional basil leaves and a drizzle of cream if preferred.