Preheat the oven to 400 degrees F.
For the marinara sauce: In an 8-inch saucepan, add the olive oil along with the onion and turn the heat to medium. Add a small pinch of salt and saute until the onion softens and develops a bit of color, about 6 minutes. Add the garlic and cook for 1 minute more. Add the tomatoes along with the sugar and oregano, partially cover the saucepan with a lid, bring to a simmer and cook until the sauce reduces and deepens in color, about 20 minutes.
Remove the lid, add the basil, season with salt and pepper to taste and cook for 5 additional minutes.
For the bisque: Meanwhile, in a 9-by-13-inch glass baking dish, add the tomatoes, sugar, carrot, celery, onion, 2 tablespoons olive oil and some salt and pepper. Toss together well and roast until the veggies soften and develop some color, about 30 minutes.
Turn the heat to medium high under a large Dutch oven and add the remaining 2 tablespoons olive oil. Once heated, add the garlic and potatoes and saute until fragrant, about 1 minute. Add the roasted veggies to the Dutch oven along with the stock and marinara sauce. Bring to a simmer and simmer on low heat for 30 minutes.
Using a high-powered blender, add the soup and basil and blend until smooth and creamy (you will have to do this in batches). Transfer the creamy soup back to the pot and stir in the Parmesan and cream. Garnish with the mascarpone and more Parmesan.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.