1. Heat the oven to 425 degrees.
2. Use a fork to lightly pierce each potato several times. Bake until completely soft, about 40 to 60 minutes. Cut each potato in half and scoop out flesh. Discard the skins.
3. In a large bowl, combine the potato flesh and just enough flour to form a smooth dough that is not sticky. All the flour may not be used, depending on the starchiness of the potatoes.
4. Form the dough into thin cylinders, then cut them with a knife into pieces about 1 inch long.
5. Using your thumb, press each piece of dough against a floured fork, then let it fall onto the work surface. When all the pieces have been made, cover them with a cloth and let them rest.
6. Meanwhile, in a medium saucepan over medium, heat the olive oil. Add the onion and mushrooms and saute until the onions are golden. Add the tomato paste mixture and red wine, if using.
7. Add the broth, reduce the heat to low, and cook slowly, stirring occasionally, adding a little more broth if the mixture dries out.
8. While the sauce cooks, bring a large saucepan of salted water to a boil. Add the potato dumplings and cook just until they float. Use a slotted spoon to transfer them to a deep serving dish, alternating them with layers of the sauce. If desired, sprinkle with cheese.
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