Bake potatoes until very soft on a bed of coarse salt in a baking dish, about 45 minutes. (The salt keeps the potatoes from touching the dish and developing a hard spot.) Cool potatoes until warm, then halve lengthwise and scoop out the flesh. Pass the flesh through a food mill or ricer, or push it through a coarse sieve. You should have about 4 cups.
In a bowl, combine potato, egg yolks, Parmesan, salt, pepper, and nutmeg. Work the mixture with a wooden spoon until smooth. Add 1 cup of the flour and knead very gently, patting and pressing the dough with your hands until all the flour is incorporated. Add some or all of the additional 1/4 cup flour if the dough feels too moist, it should be soft but shouldn't stick to your hands. Transfer dough to a work surface and roll into a log about 3 inches in diameter. Cut the log into 8 equal pieces.
Give each piece a quarter-turn so that you are rolling the dough in a different direction, then roll into ropes, a generous 1/2-inch in diameter, as if making breadsticks. Flour the ropes generously, and then cut crosswise at 1/2-inch intervals. You can shape the gnocchi on a ridged butter paddle or on the back of a fork, or you can cook them as is. Let them dry at room temperature for at least 20 minutes before cooking.
Heat a large saute pan over high heat. When hot, add oil, and then sprinkle in the mushrooms. Don't stir! Let the mushrooms sizzle and caramelize for 7 to 8 minutes. Stir and season with salt and pepper. Add garlic and cook, stirring, for about 1 minute to release its fragrance. Add the rosemary and shallot and cook for about a minute. Cook briefly to release their fragrance, then add tomato and red wine and simmer until almost evaporated. Add the broth or water. Simmer until slightly reduced, 4 to 5 minutes. Season, to taste, with salt and pepper. Remove from heat and stir in the butter. Sprinkle with the parsley and keep warm.
Bring a large pot of salted water to a boil. Add the gnocchi. They are usually done about 2 minutes after they float to the surface, but test 1 to be sure. Lift them out with a skimmer and transfer to a large platter. Pour the warm sauce over the gnocchi. Grate Parmesan over the top and serve immediately.