In a medium saucepan, bring chicken broth to a rolling boil over medium-high heat. Stir in spinach leaves, dark sesame oil, and salt, allowing the spinach to wilt into the soup. Stir well until the chicken broth is swirling in circles. Slowly pour beaten eggs into soup, and continue to stir gently for about 30 seconds. Sprinkle thinly sliced scallions onto the soup, and serve hot.