On a clean work surface, mound the flour and create a wide well in the center. Add the eggs, olive oil, and salt into the well.

Using a fork, gently beat the eggs, gradually drawing in flour from the inner walls of the well. Continue until the mixture becomes a shaggy dough.

Using your hands, bring the dough together and knead for 8-10 minutes until smooth, elastic, and slightly tacky but not sticky. If too dry, add water a drop at a time; if too sticky, dust with flour.

Wrap the dough tightly in plastic wrap and let it rest at room temperature for 30 minutes. This relaxes the gluten, making it easier to roll.

Cut the dough into 4 equal pieces. Keep unused portions covered. Flatten one piece and, on a lightly floured surface, roll it through a pasta machine starting at the widest setting, folding and re-rolling until smooth. Gradually reduce the thickness to your desired setting (usually #6 for fettuccine).

Lay the rolled sheet flat and cut into fettuccine or tagliatelle noodles using the machine's cutter attachment or by hand with a sharp knife. Toss the cut pasta lightly with flour and form into loose nests.

Bring a large pot of generously salted water to a rolling boil. Add the fresh pasta and cook for 2-3 minutes until al dente and fully cooked through; an instant-read thermometer inserted into a strand should read at least 160°F (71°C) to ensure the eggs are safe. Reserve 1 cup of pasta water before draining.