01 - Heat olive oil in a large saucepan over medium heat. Add chopped onion and diced carrot; sauté for 5 minutes until softened and fragrant.
02 - Stir in minced garlic and cook for 1 minute until aromatic, being careful not to burn.
03 - Add canned tomatoes with juice, vegetable broth, sugar if using, salt, and pepper. Bring mixture to a gentle simmer, stirring to incorporate all ingredients.
04 - Reduce heat to low, cover saucepan, and simmer for 20 minutes. Stir occasionally to prevent sticking and ensure even cooking.
05 - Remove saucepan from heat. Add fresh basil leaves and let steep for 2-3 minutes to infuse flavor.
06 - Using an immersion blender, puree soup directly in the saucepan until completely smooth and velvety. Alternatively, work in batches using a countertop blender.
07 - Stir in heavy cream until fully incorporated. Taste and adjust seasoning with additional salt and pepper as needed.
08 - Reheat gently if necessary. Ladle into bowls and garnish with additional fresh basil leaves. Serve immediately while hot.