01 - In a large saucepan, heat olive oil over medium heat. Add onion and carrot; sauté for 5 minutes until softened.
02 - Add garlic and cook for 1 minute until fragrant.
03 - Stir in the tomatoes (with juice if using canned), vegetable broth, sugar (if using), salt, and pepper. Bring to a simmer.
04 - Reduce heat, cover, and simmer for 20 minutes, stirring occasionally.
05 - Remove from heat. Add the basil leaves.
06 - Using an immersion blender (or working in batches with a countertop blender), puree the soup until smooth.
07 - Stir in the cream and adjust seasoning to taste.
08 - Reheat gently if needed. Serve hot, garnished with extra basil.