Begin by making the pasta. Using a stand mixer: Add the flour, eggs, salt and olive oil to the bowl of a stand mixer fitted with the flat beater attachment. Turn the mixer to low and beat until the ingredients are incorporated. If necessary, add water 1 Tablespoon at a time until the dough comes together. Then replace the beater attachment with the dough hook and knead for 5-6 minutes. By hand: Place the flour in a mound on your work surface, form a well in the middle and add the eggs, salt and olive oil. Then, using a fork, break the egg yolks and lightly scramble the eggs. Using your fingers, gradually incorporate the ingredients until they form a dough. If necessary, add water 1 Tablespoon at a time until the dough comes together. Then, knead the dough for 5-6 minutes.
Allow the dough to rest for 30 minutes before continuing.
After the dough has rested cut off an egg sized chunk of dough and cover the remaining dough so it doesn’t dry out. Dust the dough with flour, flatten it into a disk and run it through on the widest setting on the roller.
Adjust the setting to the next widest setting and repeat. If the dough sticks to the rollers, or it looks pitted as it comes out the bottom of the roller, the dough is too sticky. Dust it with flour and roll again.
Continue this process until the dough is about 1/4" thick. On my kitchen aid attachment, it's number 4. Using the pastry cutter, trim the ends of the sheet so they are square. Cut the sheet so they are about 12" -16" long.
Lay two sheets of pasta down on a large work surface. Arrange the parsley leaves on top of one sheet of dough and then cover with the other sheet. Press firmly so the parsley doesn't slip when you pick up the sheets.
Turn your pasta machine back one setting and carefully, run the pasta sheets through the roller again. This time, they will come out laminated.
Sprinkle with flour and then wrap the pasta sheets into loose rolls, without pressing, seam side up. Using a knife, cut the pasta into 1/4" wide strips. Unwrap the rolls by gently picking up the end of the fettucine and allowing them to unravel. Then, wind them into a nest and let them dry on a lightly floured work surface.
Then, make the sauce. Add the pine nuts, garlic, parsley and salt to the bowl of a stand mixer. Blitz until the ingredients are well combined. Then, add the extra virgin olive oil or softened butter and pulse until well combined. Alternatively, this can be done using a mortar and pestle.
When you are ready to cook the pasta, bring a pot of salted water to a rolling boil.
Add the pasta and boil for 3-4 minutes or until the pasta rises to the top.
When the pasta is cooked, strain and transfer to a large mixing bowl. Add the sauce and toss until the pasta is evenly coated. Note: If you used butter instead of olive oil, you may want to thin the sauce with a bit of pasta water.
Plate the pasta, scatter more pine nuts over the top and enjoy!