01 - Preheat the oven to 400°F. Line a baking sheet with parchment paper.
02 - Arrange the halved tomatoes cut side up, onion, carrot, and garlic on the prepared baking sheet. Drizzle with olive oil and sprinkle lightly with salt and pepper.
03 - Roast for 30 to 35 minutes, until vegetables are caramelized and tender.
04 - Transfer the roasted vegetables to a large pot. Add vegetable broth, tomato paste, sugar, salt, pepper, and dried oregano if using. Bring to a boil, then reduce heat and simmer for 10 minutes to meld flavors.
05 - Add the fresh basil leaves. Using an immersion blender or working in batches with a countertop blender, blend the soup until smooth and creamy.
06 - Stir in the heavy cream. Taste and adjust seasoning if needed. Ladle soup into bowls, garnish with extra basil, and serve hot.