Begin by preheating your oven to 400°F (200°C), setting the stage for roasting.
On a large baking sheet, place the halved tomatoes with the cut side facing up, along with the quartered red onion and unpeeled garlic cloves.
Drizzle the olive oil over the arranged vegetables, ensuring an even coating. Then, sprinkle the dried oregano, sugar, salt, and pepper generously over everything for flavor enhancement.
Transfer the baking sheet to the preheated oven and roast for 30-35 minutes. You're looking for the tomatoes to become caramelized and the onions to soften beautifully.
Once roasted, carefully remove the baking sheet from the oven and allow it to cool slightly. Squeeze the roasted garlic from its skins, discarding the skins afterward.
In a large saucepan, combine the roasted vegetables, which will be bursting with flavor, along with their juices and the vegetable broth. Place the saucepan over medium heat and bring the mixture to a gentle simmer.
Using an immersion blender, purée the soup until it's smooth and creamy. If you prefer a bit of texture, you can blend only half of the mixture in a regular blender, then return it to the saucepan.
Stir in the torn fresh basil and the heavy cream, if you're using it. Taste and adjust seasoning with additional salt and pepper as needed. Let the soup heat through for about 5 minutes.
Ladle the soup into bowls and serve it hot, garnished with extra basil leaves for freshness and a light drizzle of olive oil if desired.
Notes
Serve in rustic bowls with a swirl of cream and fresh basil. A side of crusty bread pairs well.