Heat the oil and butter in a large dutch oven over medium-high heat until the butter is melted. Add the onion and saute for 5-6 minutes until softened. Add the garlic and saute another 30 seconds.

Add the sugar, salt, oregano, dried basil, pepper, red pepper flakes, tomato paste, and balsamic vinegar, if using.

Add the whole tomatoes and diced tomatoes, with juices, along with the chicken broth. Bring to a boil, then reduce the heat to low and simmer for at least 15 minutes, although 30-45 minutes is preferable.

Remove from heat and transfer ½ of the soup to a blender. Cover with a towel (not the lid, which will create too much pressure build-up from the heat of the soup) and blend until smooth. Repeat with the remaining soup. Or use an immersion blender, if you have one.

Stir in the cream, basil, and parmesan. Serve with additional cream swirled over the top of the soup and extra sprinkles of chopped basil.