Bring 6 quarts water to boil and add 2 tablespoons salt.
Place the noodles in boiling water and allow 8 to 9 minutes to cook. In a 12 to 14-inch saute pan, place the oil, anchovies and onion over medium heat and cook until onions are caramelized. Stir often to break up the anchovies until a paste is formed, about 8 to 10 minutes. Add the milk. Drain the pasta and toss into the pan. Add the parsley, toss over high heat 1 minute and place on a plate. Serve immediately.
Make a mound 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 milk mixture. Using a fork, beat together the eggs and milk mixture and begin to incorporate the flour starting with the inner rim of the well.
As you expand the well, keep pushing the flour up to retain the well shape. Do not worry that this initial phase looks messy. 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 any leftover crusty bits. Discard these bits. Lightly flour the board and continue kneading for 3 more minutes. The dough should be elastic and a little sticky. Continue to knead for another 3 minutes, remembering to dust your board when necessary. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature. Note: Do not skip the kneading or resting portion of this recipe. They are essential for a light pasta.
To make the Bigoli: Cut the dough into 6 pieces, and run each piece through a meat grinder set to the smallest extrusion size. As the pasta exits, cut it into 12-inch pieces and immediately dust with flour. Lay out on a cookie sheet dusted with cornmeal, being careful to keep the strands separate. Finish all 6 pieces the same way.