Break up the duck carcass into 3 pieces and add it to a large pot with any remaining bones. Fill with water until the carcass is covered, then add the onions with their skin, the parsley stalks, porcini mushrooms, garlic, thyme, bay leaves and peppercorns.
Heat the pan to a very gentle simmer, cover and leave to cook for two hours, occasionally skimming the scum from the top.
Strain the stock carefully through a colander and then through a sieve before adding the stock back into the pan with carrots and celery. Bring up to a mild simmer again and season generously with salt. Cook for 10 minutes until the vegetables are tender, then add the beans, pearl barley and chard. Cook for a further 5 minutes.
Add the sherry with any reserved duck meat and cook for 2 more minutes. Divide between serving bowls and serve with sourdough bread, grated Parmesan and olive oil.