Rinse the livers and cut them into even bite-sized pieces. In a large, heavy-bottomed pot, heat the olive oil over a medium-hot flame until hot but not smoking. Add onion and the livers and cook until lightly browned, about 3 to 4 minutes. Season, to taste, with salt and pepper.
Add the wine and bring it to a full boil. Lower the heat and let the broth simmer gently, until greatly reduced to a thicker ragu consistency, about 15 to 20 minutes. Add the broth and the prepared bigoli and cook until al dente.
To serve, divide the bigoli and ragu evenly among 4 warmed pasta bowls.
Sift together the flour and salt. Make a mound of the flour mixture in the center of a large wooden cutting board. Make a well in the middle and carefully add the eggs and milk into the well. 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 1 hour at room temperature.*
To make the Bigoli:
Cut the dough into 3 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 3 pieces the same way.
*Do not skip the kneading or resting portion of this recipe. They are essential for a light pasta.