01 - Heat olive oil in a large pot over medium heat. Cook diced onion, stirring occasionally, until soft and translucent, about 5 minutes.
02 - Add minced garlic and cook for 1 minute until fragrant.
03 - Stir in chopped tomatoes with their juices or canned tomatoes, vegetable stock, sugar, salt, black pepper, and oregano if using. Bring to a boil, then reduce heat and simmer uncovered for 25 minutes, stirring occasionally.
04 - Remove pot from heat and stir in fresh basil leaves.
05 - Use an immersion blender to purée the soup directly in the pot until smooth, or blend in batches in a countertop blender after cooling slightly.
06 - Return the soup to low heat. Stir in heavy cream and gently warm without boiling.
07 - Taste and adjust salt and pepper as needed. Ladle into bowls, garnish with additional basil leaves, and serve hot.