Preheat oven to 220°C (425°F). Arrange halved tomatoes cut side up on a large rimmed baking sheet. Scatter onion quarters and unpeeled garlic cloves in the gaps. Drizzle with 2 tablespoons olive oil. Season with salt and pepper. Sprinkle optional brown sugar over the tomatoes only.
Roast on the center rack for 35 to 40 minutes until tomato surfaces are deeply caramelized to dark red with amber-brown edges and the surrounding pan is coated with thick, sticky tomato juice.
Using a silicone spatula, scrape all roasted tomatoes, onion, and accumulated pan juices into a large pot. Squeeze roasted garlic from their skins directly into the pot; discard skins.
Add vegetable broth to the pot. Bring to a gentle boil over medium-high heat, then reduce and simmer uncovered for 10 minutes.
Turn off heat. Blend in batches in a countertop blender on high speed for 90 seconds per batch, filling each batch no more than halfway. Or use an immersion blender directly in the pot for 2 to 3 minutes.
Return blended soup to the pot over low heat. Stir in heavy cream and optional butter. Heat gently for 3 to 4 minutes until fully incorporated and steaming. Taste and adjust seasoning.
Ladle into warmed bowls. Garnish with a cream swirl, fresh basil leaves, and a drizzle of olive oil. Serve immediately.
