In a large, heavy saucepan, heat the olive oil over medium-high heat. Add carrots, onion, and basil. Cook until vegetables are softened, about 10 minutes.
Add tomatoes and broth, bring to a boil, then reduce heat and simmer 30-40 minutes.
Remove from heat and allow soup to cool slightly. Puree soup a blender or food processor until smooth, in batches if necessary. Pour pureed soup back into to pot.
Stir cream into soup, a little at a time, over low heat, until desired texture is reached and soup is just heated through. Season to taste with salt and pepper, and serve warm.
