1 3/4 cups (8 ounces) all-purpose flour
6 large egg yolks
1 large egg
1 1/2 teaspoons olive oil
1 tablespoon milk
By hand: Mound the flour on a board or other surface and create a well in the center, pushing the flour to all sides to make a ring with sides about 1 inch wide. Make sure that the well is wide enough to hold all the eggs without spilling.
Pour the egg yolks, egg, oil, and milk into the well. Use your fingers to break the eggs up. Still using your fingers, begin turning the eggs in a circular motion, keeping them within the well and not allowing them to spill over the sides. This circular motion allows the eggs to gradually pull in flour from the sides of the well; it is important that the flour not be incorporated too rapidly, or your dough will be lumpy. Keep moving the eggs while slowly incorporating the flour. Using a pastry scraper, occasionally push the flour toward the eggs; the flour should be moved only enough to maintain the gradual incorporation of the flour, and the eggs should continue to be contained within the well. The mixture will thicken and eventually get too tight to keep turning with your fingers.
When the dough begins thickening and starts lifting itself from the board, begin incorporating the remaining flour with the pastry scraper by lifting the flour up and over the dough that's beginning to form and cutting it into the dough. When the remaining flour from the sides of the well has been cut into the dough, the dough will still look shaggy. Bring the dough together with the palms of your hands and form it into a ball. It will look flaky but will hold together.
Knead the dough by pressing it, bit by bit, in a forward motion with the heels of your hands rather than folding it over on itself as you would with a bread dough. Re-form the dough into a ball and repeat the process several times. The dough should feel moist but not sticky. Let the dough rest for a few minutes while you clean the work surface.
Dust the clean work surface with a little flour. Knead the dough by pushing against it in a forward motion with the heels of your hands. Form the dough into a ball again and knead it again. Keep kneading in this forward motion until the dough becomes silky-smooth. The dough is ready when you can pull your finger through it and the dough wants to snap back into place. The kneading process can take anywhere from 10 to 15 minutes. Even if you think you are finished kneading, knead it for an extra ten minutes; you cannot over-knead this dough. It is important to work the dough long enough to pass the pull test; otherwise, when it rests, it will collapse.
Double-wrap the dough in plastic wrap to ensure that it does not dry out. Let the dough rest for at least 30 minutes and up to 1 hour before rolling it through a pasta machine. The dough can be made a day ahead, wrapped and refrigerated; bring to room temperature before proceeding
For the Carbonara:
1 small head cauliflower, cut into florets
10 ounces mushrooms, quartered
1 large red pepper, diced
1 tablespoon olive oil
4 ounces pancetta, diced or 4 ounces bacon cut into 1 inch pieces
1 clove garlic, chopped
1/2 cup (2 ounces) parmigiano reggiano (parmesan), grated
Fresh black pepper
Salt to taste
1 tablespoon parsley, chopped
Toss the cauliflower and mushrooms in the oil, salt and pepper, place on a baking sheet in a single layer and roast in a preheated 400 degree oven until they start to caramelize, about 20-30 minutes, mixing half way through.
Start cooking the pasta as directed on the package.
Cook the pancetta in a pan, pour off all but a tablespoon of the grease from the pan, add the garlic, cook for 30 second and turn off the heat.
Mix the egg, cheese, pepper and salt and parsley in a bowl.
Drain the cooked pasta reserving some of the water.
Mix the pasta, egg mixture, cauliflower and mushrooms into the pan with the pancetta, adding reserved pasta water as needed.