Put the flour on a clean work surface and make a well in the middle. In the well, add the whole egg, yolks, milk, and butter. Stir with a fork, gradually incorporating the flour until it can be managed by hand. Knead the dough for at least 5 minutes before incorporating any additional water. Knead for a total of at least 10 minutes. Once thoroughly kneaded, make a ball, and flatten it slightly into a disc, wrap with plastic and refrigerate for at least 30 minutes and up to several hours.

After the dough has rested, remove from the refrigerator. Knead the dough for a minute to warm it up and make it pliable. At this point, you can divide the pasta into quarters and roll each piece out on a pasta roller or on a lightly floured surface with a rolling pin. Roll the pasta out very thin (we roll it to a level 5 on our pasta roller). You should be able to see light through the pasta sheet when you hold it up.

After rolling out each sheet, lightly flour your work surface and fold the pasta sheet in half, then in half again, and again until your folded sheet is about 3 inches wide. Using a sharp knife, cut the ribbons with a knife to about ¼ to ⅓ of an inch wide (6-8mm). Sprinkle with extra flour and set them aside while you roll out the next sheet.

Once all the pasta has been cut, you can leave it at room temp while you make your sauce. You can also make the pasta in advance and place it in the fridge up to 24 hours before cooking the pasta. Or immediately freeze fresh pasta and use within 6 months.

To a large pan, add the oil to coat the bottom over medium heat. Add the sausage and break it up as it cooks with a wooden spoon. Cook until browned and almost cooked throughout, about 5 minutes. Just before the sausage is finished cooking, drain off the excess fat rendered from the sausage – leaving behind about a tablespoon. Add the onion at this point and cook until the onions are translucent, about 5-7 minutes.

Add the rosemary, fennel seeds, cloves, and cream to the sausage and stir. Turn the heat off and set aside.

In a separate large skillet, melt the butter over medium to medium-high heat until it stops foaming. Add the mushrooms and cook, stirring often, until the mushrooms are tender and have begun to brown, about 5-7 minutes. Add the garlic, pepper, and salt, stir and cook for about 30 seconds. Pour in the vermouth and wine to deglaze and cook until most of the liquid has evaporated, about 3-4 minutes.

Add the mushroom mixture to the sausage and cream mixture and stir. Stir in the lemon juice and parsley. Keep this mixture on low while you cook the pasta. When the pasta is almost done, add the truffle oil and Parmesan to the sauce. The sauce will be thick and creamy and can be thinned slightly with water from the pasta when the tagliatelle is finished.

Bring some salted water to a hard boil and add the tagliatelle. Cook for about 2-3 minutes (for fresh pasta only - see note for cooking store-bought pasta), taste for doneness. Remove the tagliatelle to a large serving bowl and toss with the sauce to combine. Use a small amount of the pasta water to thin out the cream sauce if necessary.

You can garnish with chopped oregano leaves, red pepper flakes, parmesan cheese, or toasted breadcrumbs.