In a 6 to 8 quart heavy-bottomed pot, heat the olive oil over medium heat until hot. Add the onions, celery, carrots and garlic and cook until the vegetables are translucent but not browned, about 5 minutes. Add the veal, pork and pancetta, increase heat to high, and brown the meat, stirring frequently. Add the tomato paste, milk, wine, and thyme and bring just to a boil, then reduce the heat to medium-low and simmer for 1 to 1 1/2 hours.
Season the ragu with salt and pepper, remove from the heat, and let cool if not using immediately. (The ragu can be refrigerated for up to 2 days; it can also be frozen for up to 1 month).
Toss with the green tagliatelle and serve, garnished with cheese, if desired.
Bring 3 quarts of water to a boil in a large pot, and add 1 tablespoon salt. Set up an ice bath next to the stove. Blanch 1 cup packed spinach leaves in the boiling water for 45 seconds, then remove with tongs or a slotted spoon and immediately plunge into the ice bath to cool for 2 minutes. Drain the spinach and squeeze dry in a kitchen towel, removing as much moisture as possible. Chop the spinach very fine and combine with the eggs in a small bowl. Stir well until as smooth as possible.
Mound the flour in the center of a large wooden board. Make a well in the center of the flour and add the egg and spinach mixture to the well. Begin to incorporate the flour into the egg and spinach mixture, 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 if it looks messy). When half of the flour is incorporated, the dough will begin to come together. Start kneading the dough, using primarily the palms of your hands. Once the dough is a cohesive mass, set the dough aside and scrape up and discard any dried bits of dough.
Lightly flour the board and continue kneading for 10 minutes, dusting the board with additional flour, as necessary. The dough should be elastic and a little sticky. Wrap the dough in plastic wrap and allow to rest for 30 minutes at room temperature before using.
Use the wider cutter attachment of the pasta machine to cut the sheets into 1/2-inch-wide strips. Or, to cut the pasta by hand, cut each sheet of pasta into 10-inch lengths. Brush lightly with flour, then roll up the sheet, and, using a sharp knife, cut into 1/4-inch-wide strips; unroll.
Cook pasta in a large pot of boiling salted water until al dente.
Yield: about 1 1/4 pounds