01 - Heat olive oil in a large pot over medium heat. Add onion and cook for 5 minutes, until soft and translucent.
02 - Stir in garlic and cook for 1 minute until fragrant.
03 - Add chopped tomatoes with their juices if using canned and cook for 5 minutes, stirring occasionally.
04 - Pour in vegetable broth. Bring to a boil, then reduce heat and simmer uncovered for 20 minutes, until tomatoes are very soft.
05 - Remove from heat. Add most of the basil leaves, reserving a few for garnish.
06 - Blend the soup using an immersion blender or carefully in batches in a regular blender until smooth.
07 - Return the soup to low heat. Stir in heavy cream and sugar if using. Season with salt and pepper to taste. Heat gently until warmed through—do not boil.
08 - Ladle into bowls, garnish with extra basil leaves, and serve hot.