01 - Heat olive oil in a large saucepan over medium heat. Add chopped onion and diced carrot; sauté for 5 minutes until softened and translucent.
02 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to brown it.
03 - Pour in canned tomatoes with their juice, vegetable broth, sugar if using, salt, and pepper. Bring the 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 let them steep in the hot soup for 2-3 minutes.
06 - Using an immersion blender, puree the soup until completely smooth and velvety. Alternatively, work in batches using a countertop blender, filling only halfway and venting lid.
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 fresh basil leaves. Serve immediately with crusty bread.