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To prepare the tagliatelle, place the flour in a mound on a pasta board or clean work surface.
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Using your fingers, make a center well.
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Place the eggs, oil, salt, and 1 tablespoon water in the well.
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Again using your fingers, mix the liquid ingredients together.
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Then begin pulling in flour from the inside rim of the well.
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Continue to pull the flour into the liquid until it is mostly mixed together.
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Using both hands, gather the mixture together in a ball and begin kneading it, picking up stray pieces of dough as you work it.
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Continue kneading until you have a smooth, elastic ball, about 5 minutes.
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Wrap the dough in plastic wrap and refrigerate it to rest for 30 minutes.
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Meanwhile, to prepare the Bolognese sauce, heat the olive oil in a large skillet over high heat.
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Add the ground beef and cook, breaking up the chunks with a spatula, until it is evenly browned, about 7 minutes.
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Use a slotted spoon to transfer the meat to a plate; set aside.
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Return the skillet to medium heat and add the pork (or pork and pancetta).
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Cook, stirring frequently, until just cooked through, about 2 minutes.
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Add the carrot, onion, celery, and garlic and cook until the vegetables are tender, about 4 minutes.
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Return the ground beef to the skillet.
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Add the wine, stock, tomato paste, tomatoes, thyme, rosemary, half of the parsley, and the salt and pepper.
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Bring to a boil.
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Then lower the temperature to a slow simmer, cover, and cook for 40 minutes.
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For a creamier, thicker Bolognese sauce, whisk just enough of the milk into the flour to make a creamy paste.
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Whisk in the remaining milk, and then pour the mixture into the simmering Bolognese sauce; cook, stirring often, for 5 minutes.
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(You can store the sauce, covered and refrigerated, for up to 4 days, or freeze it in a quart container for up to 2 months.)
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If cooking the pasta immediately, keep the sauce at a low simmer.
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Line a sheet pan with parchment paper.
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Set the pasta machine roller on the widest setting.
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Cut the ball of dough into 2 pieces.
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Flatten one of the pieces of dough into a rectangle and feed it through the pasta machine rollers.
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Fold the ends into the center (as if you were closing a book), and feed the pasta through the rollers again with the seam vertical.
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Repeat two or three more times to widen the pasta sheet, and then send the sheet (without folding) through the pasta machine six or seven more times, gradually lowering the setting and lightly dusting with flour to prevent sticking, until you have a long, paper-thin sheet of pasta.
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Cut this sheet into 12-inch rectangles and place them on the parchment paper.
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Repeat the whole process with the second piece of dough.
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Fit the pasta machine with the tagliatelle attachment (fettuccine and tagliatelle are generally interchangeable).
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Roll each pasta sheet through the machine.
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Toss the long strands with some cornmeal to prevent sticking until ready to cook.
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Bring a large pot of water to a boil and season it with salt.
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Cook the tagliatelle in the boiling water until al dente, 2 to 3 minutes.
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Drain, and quickly return the pasta to the pot; it should still have some cooking water on it.
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Add the hot Bolognese sauce, the Grana Padano, and the remaining parsley, and stir or toss to combine.
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Serve immediately, piping hot.
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Variations
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Omit the pork or pancetta and add more beef.
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Enjoy the Bolognese between layers of lasagna or on top of Parmesan risotto.
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We offer the option of fresh traditional or whole-wheat tagliatelle; enjoy the Bolognese with either.
