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For the dough: Wash and dry your hands. Place the flour in center of your work surface. Create a well in the center. Crack the eggs into a bowl and whisk very well with some salt, about 1 minute. Add the eggs into the flour well. Slowly incorporate the flour into the eggs with your fingers or a fork. When there is no liquid egg left, start forming a ball with the loose dough. After the dough ball is formed, you must start to knead the dough using the base of the palm of your hand. Push into the dough and turn, and then fold the dough into itself. Knead to develop the gluten in the flour, 5 to 7 minutes, this will help for the perfect 'al dente' texture when the pasta is cooked. When the dough ball is smooth, wrap in plastic, rest in the refrigerator for at least 1 hour.
Cut the pasta into palm-size pieces so they will pass through pasta machine easily. Press one edge of the pasta piece flat so it will fit through the rollers of the pasta machine set on the widest setting. Feed the dough through the machine on each setting from widest to second thinnest, sending the pasta through each setting twice. As the sheet of pasta forms, you want to fold the ends in on to itself and feed it back through the machine. This will create a nice square edge. If the sheet becomes to long and difficult to handle, cut it shorter. Use the backside of your hand to support the pasta coming out of the machine so it doesn't sag and stretch. The final thickness for fettuccine should be just less than a coaster, about 1-millimeter thick. You can hang the sheets to dry or place them on trays lined with kitchen towels.
For the pasta: Bring a large pot of salted water to a boil.
Heat a frying pan over medium-high heat, and add the pancetta. Cook until the fat is rendered and the pancetta is brown, 3 to 5 minutes. Remove the pancetta from pan, place on a paper towel, and set aside for later (reserving some of the pancetta for garnish). Keep the fat in the pan, and turn down the heat to medium. Add garlic and onions to the pancetta fat and cook 3 minutes. Then add the mushrooms, and cook until the water evaporates, 10 minutes. Season with salt and pepper.
Add the cooked pancetta and the peas to the pan, stirring to incorporate everything together. Cook 2 to 3 more minutes.
Drop the nests of fettuccine into the boiling water, and cook until al dente, 2 minutes. Then remove the pasta from the boiling water and reserve 1/2 cup of the pasta water.
Add the cooked pasta to the frying pan with pancetta mix, then add in the reserved pasta water and the grated cheese, saving some for garnish. Stir, then shut off the heat and add the egg yolks, and stir. You DO NOT want to scramble the yolks, you should have a beautiful smooth coating ton the fettuccine now. Garnish with the reserved crispy pancetta, grated cheese and some chives. Buon Appetito!!