Combine the broth and barley in a soup pot and bring the liquid to a simmer over medium heat Add each vegetable to the pot as you prepare it; peel the potato and turnip and cut them into 3/4 inch chunks. Dice the celery, peel and slice the carrots into rounds, 3/4 inch thick.
When all of the vegetables are in, bring the liquid to a boil, then cover and reduce the heat and simmer gently for 30 minutes.
Meanwhile thinly slice the scallions, including 4 inches of the green tops. Rinse and coarsely chop the escarole.
Add the beans to the soup; season to taste with salt and pepper. Simmer, covered 15 minutes longer. Add the escarole and scallions and simmer until wilted, about 2 minutes.
Adjust the seasoning and serve very hot with grated Parmesan on the side.