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 but not browned.
03 - Add canned tomatoes with their juice, vegetable broth, sugar (if using), salt, and pepper. Bring mixture to a gentle simmer.
04 - Reduce heat to low, cover, and simmer for 20 minutes. Stir occasionally to prevent sticking and ensure even cooking.
05 - Remove from heat. Add fresh basil leaves and allow to steep briefly in hot liquid.
06 - Use immersion blender to puree soup until completely smooth. If using countertop blender, work in batches and vent steam carefully.
07 - Stir in heavy cream until fully incorporated. Taste and adjust salt and pepper as needed.
08 - Reheat gently over low heat if necessary. Serve hot in warmed bowls, garnished with additional fresh basil leaves.