Boil four cups of water. Place the dried porcini in a heatproof pan and pour the boiling water over them. Let sit until very soft, about 30 minutes to one hour. Strain through a very fine mesh sieve or coffee filter. (Taste a mushroom. If it is at all gritty, rinse and drain them again). Finely chop the mushrooms. Set both broth and mushrooms aside.

Preheat oven to 350 degrees. Poke the sweet potatoes in several places with a fork. Place the sweet potatoes on a baking sheet. Bake until tender, about 40 minutes. Peel and pass through a ricer into a large bowl, or mash well. Combine sweet-potato puree, flour, salt and pepper. Place the dough on a lightly floured surface. Knead the dough, adding more flour if needed, until it is smooth and slightly sticky.

Divide the dough in two. Ona. lightly floured board, roll each half into a rope about 1/2 inch in diameter. Using a sharp knife, cut 1/2 inch pieces off the roll and set aside on a floured surface. You can roll each piece against a gnocchi shaper or press them gently with your thumb to give them some shape. Repeat with the remaining dough pieces until done. Shape the dough into small dumplings. Set aside.

Bring a large pot of salted water to a boil, then reduce to a steady simmer. Working in batches, drop the gnocchi into the water. Cook 10 seconds after the dumplings rise to the surface, about 5 minutes total. Remove with a slotted spoon to a large warm serving bowl. Toss with the shredded chard, mushrooms and ricotta salata. Sprinkle with Parmesan and serve.