1. Stir together the flour and salt in the bowl of a stand mixer. Add the egg, egg yolk, and water. Mix the dough with the dough hook, kneading it for 8 to 10 minutes, until it comes together in an integrated mass that clings to the hook. If the dough looks shaggy and dry, add more water by the tablespoon.

2. Remove the pasta dough from the bowl and knead it by hand on a lightly floured surface for a minute or so to bring it together and smooth it out. The resulting ball of dough should be smooth and resilient: it should spring back when poked. Wrap the dough in plastic wrap and let it rest for an hour or two (or as long as overnight) in the refrigerator.

3. Clamp the pasta machine onto the edge of your counter or work surface. Cut the ball of pasta dough into 3 pieces and lay a damp kitchen towel over them to keep them from drying out or forming a skin while you roll the dough into sheets. Use your hands to shape one piece of the pasta dough into a rough rectangle just wide and compact enough to fit through the rollers of the pasta machine. Roll the pasta through the widest setting six or seven times, folding it over end to end or creasing it down the middle after the first pass and cranking it through again. Don't add flour on the first four or five passes; you want the pasta to stick to itself during this stage to build up its strength, resilience, and eventual toothsomeness. By the fifth or sixth pass, you can dust it super-lightly with flour. After the seventh pass, it should be soft, with a nice sheen to it. Continue to crank the pasta through, narrowing the rollers with each pass. For fettuccine or tagliatelle, roll the pasta through all the way down to the thinnest setting. For linguine, stop a couple of degrees shy of that. Flour the sheet and put it under a damp kitchen towel until you are ready to cut it into noodles. Repeat with the remaining dough.

4. Dust each pasta sheet with flour before cutting it into the desired shape. For fettuccine, use the wider cutter on the pasta machine; for linguine, use the thinner one. For tagliatelle, lay the pasta sheets out on a cutting board and cut them into ½-inch-wide ribbons (don't worry if they're a little irregular). Dust the cut pasta lightly with flour, arrange on a baking sheet, preferably on a lightly floured piece of parchment, and cover with plastic wrap. Refrigerate until ready to cook.

5. To cook, drop the noodles into a large pot of boiling, well-salted water. Cook for about 2 minutes after the first few noodles begin to float on top of the water. Drain, toss with the sauce of your choice, and serve.