Heat the olive oil in a soup pot over medium heat. Add the scallions and cook, stirring occasionally, for 2 minutes. Add the garlic and cook for about another minute. Add the tomatoes, stock, basil and salt and pepper.
Bring the soup to a simmer, cover the pan and cook for 10 minutes. Add the rice, cover the pan and cook for another 20 minutes.
Blend the soup in a blender or with an immersion blender. Serve hot or let cool. Stir in the milk if desired. Chill completely.
Serve garnished with fresh basil, parsley or Italian bread croutons.