Heat the olive oil in a large heavy soup pot, 4-5 quarts, over medium heat. Add the onion, leek, celery, and carrots. Cook for about 7 minutes until soft, stirring. Turn down the heat if needed, you don't want the vegetables to brown. Add the garlic and cook another minute.
Stir in the turkey, then the herbs, wild rice. Stir and cook for 3-5 minutes, then add the broth and bay leaves and bring to a simmer. Cook for about 15 minutes for flavors to blend and soup to heat through. Season with salt and pepper and soup is ready to serve.Sprinkle with parsley and parmesan if desired.
Notes
If you freeze or refrigerate this soup, you might need a little extra broth as when it sits the rice can absorb some of the broth. For brothier soup, add another cup or so of broth. If you want to make the soup ahead of time, cook the rice and store it separately from the soup so it does not get mushy and absorb a lot of broth, then add it when you're heating the soup.