Put a pot with 2 litres of water and a tablespoon of rock salt on the stove. When it comes to a boil, add the rinsed barley and the potatoes cut into large pieces. Let it simmer for 45 minutes. Clean the leek and cut it into slices. Peel and chop the celery, carrot and onion. Peel and chop the mushrooms. Put another pot on the stove with the vegetable stock and bring it to a gentle boil. Add the leek, onion, celery and carrot and cook for about 5 minutes. Add the mushrooms and cook for a further 5 minutes. Drain the barley and potatoes and pour them into the pot with the broth and vegetables, then continue cooking for another 5 minutes, taking care to mash the potatoes with a wooden spoon. Add salt to taste. Sprinkle the soup with chopped parsley and pepper and arrange it in individual bowls. Complete with grated aged strong Provolone Valpadana P.D.O. and serve.