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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.
Roll the pasta dough out to the thinnest setting on a pasta rolling machine. Cut the sheet of pasta into rectangles that are 1-inch by 2-inches. Pinch the long center of each square to form the strichettoni, or bow ties. Place the pasta on a sheet tray dusted with semolina until ready to cook, and cover with damp, clean kitchen towels.
Bring 6 quarts of salted water to a fierce boil. To finish the sauce, reheat the onion mixture over medium-high to high heat and add the cream. Stir until the cream begins to bubble. Drop the pasta in the boiling water and cook until tender yet still firm, about 3 to 4 minutes. Stir the prosciutto, parsley, scallions and herbs into the sauce. Cook only long enough to heat through -- the fresh, uncooked taste of the herbs is important here. Season to taste with salt and pepper. Drain the pasta, reserving the cooking liquid, and add it to the pan with the sauce. Add the cheese and toss over high heat 1 minute, adding a splash of pasta cooking water if necessary to keep the sauce from being too "tight". Serve in warmed pasta dishes, passing the remaining cheese separately.