A stand mixer with pasta roller and fettuccine cutter attachments (or a manual pasta machine)
Bring a large (8-quart) pot of water to a boil and add the salt. Heat a large (12-inch) saute pan over low heat and add 1/2 cup of the boiling water to the pan. Add both butters to the pan and cook for 2 to 3 minutes, stirring slowly, until the sauce has emulsified.
Meanwhile, add the Fettuccine to the boiling water and cook for approximately 1 to 2 minutes, until just tender. Using tongs, transfer the cooked pasta to the saute pan. (Do not drain the pasta water.) Add an additional 1/2 cup pasta cooking water, if required, and freshly ground black pepper to taste.
Continue to cook on low heat for 2 minutes, tossing to coat the pasta with sauce, until the sauce is well incorporated. Remove the pan from the heat and add the finely grated Parmesan in a slow steady stream while tossing the pasta. If needed, add more pasta water to loosen the sauce.
Divide the pasta among four bowls, top each serving with the aged Parmigiano-Reggiano and more freshly ground pepper and serve.
Place the 00 flour in the bowl of a stand mixer fitted with the dough hook attachment. With the mixer on low speed, gradually add the egg yolks, a few at a time. Continue to mix until the dough is smooth. If it is a touch dry, add a few drops of water. The dough will be bright yellow.
Turn the dough onto a smooth, lightly floured surface and knead by hand until it forms a smooth ball. Cover with plastic wrap and let rest at room temperature for 30 minutes.
Divide the dough into three equal portions and flatten the first portion into an oval about 3/4-inch thick. Remove the dough hook attachment from the stand mixer and attach a pasta roller attachment (or use a manual pasta roller for the next step). Set the attachment to the widest setting and run the first portion of dough through the roller. Fold the dough in on itself in thirds, rolling to knead out any air bubbles, and feed it through the roller two more times on the same setting, folding the dough in on itself and rolling between each. Change the attachment to the next setting and repeat the process, working your way through each width setting twice until the pasta is almost transparent. Repeat with the remaining pieces of dough.
Remove the pasta roller attachment from the stand mixer and attach the fettuccine attachment. Cut each rolled-out pasta sheet into 12-inch pieces and feed the pieces, one at a time, through the machine. Sprinkle the cut fettuccine lightly with flour and place in bundles on a parchment-lined sheet pan that has been sprinkled with semolina flour. Set aside until ready to use.