Bring turkey broth to a boil in a large pot. Add potatoes, carrots, and celery, and cook for about 20 mins, or until potatoes are almost tender. Add leftover turkey, green onions, salt, pepper, thyme, and sage, stir well, and return to a boil. Cook over medium heat for another 5 mins.
Meanwhile, mix evaporated milk and flour in a mixing bowl with an electric mixer. Blend milk mixture into soup. Cook, stirring constantly, until thickened (approximately 8-10 mins) Serve hot.