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.
1 recipe basic pasta dough, recipe follows
Heat the oil in a large heavy saute pan over medium heat. Add the onions, garlic and a light sprinkling of salt and pepper. Stir them lightly to coat in the oil, then cover the pan and lower the heat to the lowest possible setting. Cook 10 to 15 minutes, or until the onions are soft and almost transparent. Once the onions' natural sweetness has been accentuated by the slow cooking, you can bring out their rich savory side with browning. Uncover and raise the heat to medium-high or high. Saute the onions to deep golden brown, stirring often with a wooden spatula and scraping up the brown glaze collecting on the bottom of the pan. Take care not to let the glaze burn. If necessary, lower the heat slightly. Onions will resemble a thick, dark amber marmalade. Set aside.
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.