Sorry, grilled cheese. Quick-cooking polenta is tomato soup's new BFF.
In a large pot or soup pot, heat the oil, two turns of the pan, over medium to medium-high. Melt the butter into the oil. Add the onion, carrot, celery, garlic, thyme, and chile paste; season with salt. Cover and cook, stirring often, until softened, 4 to 6 minutes. Stir in the tomato paste, then the stock. Bring to a boil. Add the tomatoes. Bring to a boil, stirring and breaking the tomatoes up with a wooden spoon. Reduce heat to medium-low. Let the soup simmer at a low boil until the flavors meld, 8 to 10 minutes.
Using an immersion blender, puree the soup. (Or, working carefully in batches in a regular blender, puree the soup and return it to the pot.) Whisk in the polenta. Reduce heat to low. Simmer until the polenta is tender, about 2 minutes. Stir in the cream; season with salt. (If the soup gets too thick, add water to thin it.)
Serve the soup in shallow bowls. Top with the torn basil leaves and Parm.