Preheat oven to 425 degrees F.
Line a sheet pan with parchment paper, and drizzle halved Roma tomatoes with olive oil, and season with salt and pepper on both sides.
Roast cut side down for 35-40 minutes until caramelized, turning pan once if the tops start to brown quickly on one side.
Meanwhile, heat 2 tablespoon olive oil in a large stockpot or Dutch oven over medium heat.
Add diced onion and cook, stirring occasionally until softened, 5 minutes.
Add garlic and cook until fragrant, 1-2 minutes.
Add the tomato paste and stir well to incorporate with onions and garlic, and cook, stirring occasionally until it takes on a deep color, 3-4 minutes.
Add oregano, chicken stock, canned tomatoes, basil, sugar, and balsamic vinegar to the pot.
Turn heat to high, and bring to a boil.
Reduce heat to medium-low heat, cover with a lid, and simmer.
Once tomatoes are roasted, add them to the soup with remaining ingredients. Simmer 15 minutes more.
Use an immersion blender to blend the soup until smooth, then stir in cream and parmesan, and season to taste with salt and pepper.
Serve hot with additional basil leaves, and a drizzle of heavy cream, if desired.