In a large pot, heat olive oil or butter over medium heat until shimmering. Add chopped onion and diced carrot, seasoning with a pinch of salt. Sauté for about 6-8 minutes, until softened.

Stir in minced garlic and cook for another 30-60 seconds, until fragrant. Be careful not to let the garlic brown too much.

Add tomato paste to the pot, stirring well to combine. Cook for 1-2 minutes.

Pour in whole peeled tomatoes, crushing them gently, then add broth, sugar, oregano, salt, and pepper. Stir well.

Bring to a gentle boil, then reduce heat to a simmer and cook uncovered for about 15-20 minutes.

Using an immersion blender, blend the soup until smooth. If using a countertop blender, let it cool slightly first.

Stir in heavy cream and adjust seasoning with more salt or pepper if needed. Optionally add fresh basil.

Ladle the soup into bowls and serve hot, pairing with grilled cheese or a light salad.