Warm olive oil in a large pot over medium heat until it glimmers.

Add diced yellow onion and sauté for 5 minutes until translucent, then stir in minced garlic and cook an extra minute until aromatic.

Pour in chopped tomatoes, season with salt and pepper, bring to a gentle simmer, and let bubble for 10 minutes.

Use an immersion blender or countertop blender to blend until the soup is silky and lump-free.

Return the soup to low heat, stir in heavy cream and butter until melted and fully incorporated.

Turn off the heat and stir in fresh basil leaves, then adjust seasoning.

Ladle the warm soup into bowls, sprinkle with grated Parmesan and extra basil leaves, and serve with crusty bread or grilled cheese.