Melt butter in a large pot over medium; sauté onion 5 minutes until soft and translucent.
Add garlic; cook 1 minute until fragrant, stirring constantly to prevent burning.
Cook tomato paste 2 minutes to deepen flavor.
Add tomatoes with juices, broth, sugar, salt, and pepper; boil, reduce heat, and simmer 20 minutes.
Off heat, add fresh basil; puree with an immersion blender or carefully transfer to a blender in batches.
Return to pot over low; stir in cream and heat through without boiling.
Adjust seasoning to taste; serve hot with extra basil and a drizzle of cream if desired.