Heat olive oil and butter in a large pot over medium heat.
Add chopped onion and sauté for 4–5 minutes until softened and fragrant.
Stir in minced garlic and cook for another 30 seconds.
Add tomato paste and cook for 1–2 minutes, stirring, until slightly darkened.
Pour in whole peeled tomatoes with their juice and the broth.
Add sugar, dried oregano, dried basil, salt, and pepper. Stir well.
Bring the soup to a gentle boil, then reduce heat and simmer uncovered for 20–25 minutes.
Use an immersion blender (or transfer to a blender carefully) and blend until smooth and creamy.
Stir in heavy cream and adjust seasoning to taste.
Serve warm, garnished with fresh basil and a drizzle of cream.