Heat olive oil in a large pot over medium heat. Add diced onion and cook for 5 minutes until softened and translucent.
Add minced garlic and cook for 1 minute until fragrant, stirring constantly to prevent burning.
Pour in crushed tomatoes and vegetable broth. Stir in sugar, salt, and pepper. Bring to a boil, then reduce heat and simmer for 15 minutes.
Using an immersion blender, blend the soup until smooth and creamy. Alternatively, carefully transfer to a blender in batches.
Stir in heavy cream and fresh basil. Heat through for 2-3 minutes without boiling.
Taste and adjust seasoning if needed. Serve hot with a garnish of fresh basil and a swirl of cream if desired.
