Preheat oven to 450 degrees. Cut tomatoes into large chunks, removing the seeds if possible.
Place on a 21 x 15-inch baking sheet, along with the onion, carrots and garlic.
Drizzle with the olive oil, toss to coat, and season with salt and black pepper to taste.
Roast for 30-35 minutes or until the tomatoes are very soft, the onions are browned, and the carrots are soft.
Remove any tomato skins that are easy to peel off.
Transfer to a Dutch oven or other soup pot, using a rubber scraper to get every drop.
Add the chicken or vegetable broth, the rice, and thyme sprigs. Bring to a boil, reduce the heat to medium-low, and simmer for 15-20 minutes or until the liquid is slightly reduced and the rice is extremely soft.
Remove the thyme springs and let them cool to the touch. Scrape any leaves remaining on the stems back into the soup. Discard stems.
Add the chopped fresh basil and heavy cream. Using an immersion blender, puree the soup until very smooth, or puree in a blender until smooth.
Adjust seasoning with salt, pepper and sugar if needed.
Serve, garnished with cream, crushed red pepper flakes and croutons if desired.