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 and garlic 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 chile flakes and 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.
Place the leftover pasta in a large bowl. Add the butter, eggs, bread crumbs, and cheese and mix in loosely by hand or with a wooden spoon. Take handfuls of the pasta mixture and form it into lightly compressed nests of 1-inch thickness and about 4 inches in diameter. You should have about 4 to 6 nests.
In a large, heavy-bottomed skillet, heat the olive oil over high heat until it is almost smoking. Carefully place the nests in the hot oil and cook until they are golden brown and the edge is crispy. Remove from the oil, season with salt and pepper and drain on a plate lined with paper towels. Sprinkle with sugar if desired and serve immediately.
Recipe copyright 2000, Mario Batali. All Rights Reserved.