Prepare the pasta dough according to the recipe. Roll it out to the thinnest setting on a pasta rolling machine, then cut the resultant sheet into ribbons 1/4-inch wide. Place the ribbons on a sheet tray dusted with semolina and set aside, covered with clean, damp kitchen towels, until ready to cook.
Bring 6 quarts of water to a boil and add 2 tablespoons salt. In a 12 to 14-inch saute pan, heat oil until smoking. Add the onions, garlic and chili flakes and cook until light golden brown and wilted, 3 to 4 minutes. Add the mushrooms and saute over high heat 5 minutes, until golden brown. Season with salt and pepper, to taste.
Drop the tagliatelle into the boiling water and cook 1 minute. Drain the pasta, reserving the cooking liquid, and add to the pan with the mushrooms. Toss over high heat 1 minute to coat the pasta, adding a splash of the cooking water if necessary to keep the sauce from being too "tight". Add prosciutto and toss to mix. Serve immediately in 4 warmed pasta bowls, topped with Parmigiano-Reggiano.
1 recipe basic pasta dough, recipe follows
Mound 3 1/2 cups of the flour in the center of a large wooden cutting board. Make a well in the middle of the flour and add the eggs and the olive oil. Using a fork, beat together the eggs and oil and begin to incorporate the flour, starting with the inner rim of the well.
As you expand the well, keep pushing the flour up from the base of the mound to retain the well shape. The dough will come together when half of the flour is incorporated.
Start kneading the dough with both hands, using the palms of your hands. Once you have a cohesive mass, remove the dough from the board and scrape up and discard any leftover bits. Lightly reflour the board and continue kneading for 6 more minutes. The dough should be elastic and a little sticky. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature. Roll or shape as desired.