In a glass bowl, toss together the tomatoes, carrots, garlic, shallots, thyme, basil, oregano, salt, pepper, and butter until all the tomatoes, veggies, and herbs are lightly coated with the butter. Place on a parchment or silicone lined non-aluminum (important because of the acidity of the tomatoes) baking sheet or baking dish and roast in preheated oven for about 1 hour or until the skins on the tomatoes are soft, wrinkled, and lightly caramelized. Rotate the pan if necessary.
Remove from the oven and, using heat safe, non-aluminum tongs or a fork, carefully remove and discard the skins from the tomatoes.
Put all of the fruit (tomato is a fruit!), veggies, and herbs in a large saucepot. Add the stock and bring to a boil.
Reduce the heat to low and allow to simmer, covered, for 30 minutes to an hour, stirring often.
Add 1-1/2 cups cream. Using an immersion blender, puree the soup until a smooth, uniform texture results. Add up to 1/2 cup more cream to taste if desired.
Garnish with freshly chopped basil.
If you don't have an immersion blender, very carefully transfer the soup to a heat-safe blender and blend it according to the manufacturer's directions.The resulting bisque is a light orange color.