For the duxelles, heat oil in a frying pan and sauté finely chopped onion until colorless. Add very finely chopped mushrooms and sauté until there is no liquid left in the frying pan. Season strongly with chopped parsley, salt and freshly ground pepper. Season lung roast with pepper. Heat oil in a frying pan, brown lung roast heartily on all sides.
Then lift the meat out of the roasting pan and cool completely. Set the used roasting pan aside.
Roll out puff pastry to a 3 mm cornstarch (maizena) and cut to size. Spread the duxelles evenly on the pastry, place the lung roast on top and roll up tightly. Close the ends well, brush with beaten egg. Decorate the pastry case with strips of pastry, brush again with egg. Bake in oven heated to 220 °C for 30 to 40 minutes. Cover and let rest for 20 minutes while warm.
For the potato gratin, cut potatoes into 2 mm slices. Boil milk and cream, season with pepper, salt, garlic and nutmeg (freshly grated). Add potatoes and cook until crispy. Butter a gratin dish and pour in potato mixture. Sprinkle grated cheese on top and bake in oven heated to 240 degrees until golden brown.
For the sauce, sauté finely chopped onion in the drippings from the lung roast. Extinguish with Madeira, add moderate beef broth and reduce. Drain the sauce, add the liquid