Preheat the oven to 400°F (200°C).
Place the halved tomatoes, quartered onion, and garlic cloves on a large baking sheet.
Drizzle the olive oil evenly over the vegetables. Sprinkle with kosher salt, black pepper, and dried oregano.
Roast in the preheated oven for 35 to 40 minutes, until the tomatoes are soft and slightly caramelized.
Remove the baking sheet from the oven and let the vegetables cool slightly.
Transfer the roasted tomatoes, onion, and garlic to a blender. Add the tomato paste, sugar, and vegetable broth.
Blend until smooth and creamy. If the soup is too thick, add more vegetable broth to reach desired consistency.
Pour the blended soup into a large pot and heat over medium heat until warmed through, about 5 minutes.
Stir in the heavy cream and cook for an additional 2 minutes, stirring constantly. Do not boil after adding cream.
Taste and adjust seasoning with additional salt and pepper if needed.
Ladle the soup into bowls and garnish each with a fresh basil leaf before serving.