Saute the carrots and onions in the olive oil over medium heat until soft, 8 minutes.

Add the remaining ingredients and bring to a boil, then turn heat down to low, and simmer, partially covered, for about 45 minutes, until flavors are blended and vegetables are soft. Allow the soup to cool slightly. Then puree with an immersion blender or in batches in a blender until very smooth. If you like a thinner consistency, add a little bit more stock or water or milk.

Serve immediately, and garnish with more fresh basil and some grated Parmesan cheese.