To a large pot, add the broth and other simmering ingredients. Bring to a boil, then simmer about 1½ hours.
Remove the turkey carcass from the pot with tongs (and discard). Strain the broth through a fine sieve and discard the solids. Transfer the broth to a bowl; cover and set aside. You can also prepare the broth the night before and store it in the refrigerator until the next day.
MAKE THE SOUP:
In a large soup pot, heat the olive oil and then add the garlic cloves, cooking until lightly browned. Add the minced onion, carrot, celery and sweet potatoes. Saute over medium-low heat until softened, about 7 or 8 minutes.
Add the chopped sage to the soup pot along with the turkey broth and the bay leaf. Bring the mixture to a simmer. When the simmering begins, add the green beans and turkey meat to the soup. Bring it back up to a simmer. Simmer for about 5 more minutes, until the sweet potatoes are tender.
Notes
If you're preparing this recipe as gluten-free, just be sure to use chicken broth and turkey meat that are free of gluten.