In the bowl of a stand mixer, combine eggs, flour, oil and salt with your hands until a shaggy dough forms. Knead with dough hook until dough is smooth and elastic, about 10 minutes. Cover dough with plastic wrap and let rest in the refrigerator for at least 30 minutes.
Divide the dough into 4 equal portions. Attach the pasta roller attachment to the stand mixer and place it on setting 1.
Lightly dust one portion of the dough with flour, then form it into a rectangle. Pass the pasta through the rollers on setting 1 and repeat the rolling and flouring process so that the pasta passes through setting 1 a total of 4 times.
Change the rollers to setting 2, lightly flour the pasta, then pass it through the rollers. Change the rollers to setting 3, lightly flour the pasta and then pass it through the rollers. Continue with the flouring and rolling until the pasta is passed through setting 6. Repeat the rolling and flouring process with the remaining pieces of dough, placing the rolled out sheets of pasta on the floured baking sheet.
Once you've rolled out all of the dough, lay one sheet of pasta flat on your work surface. Place the sage and parsley leaves on the dough, spacing them in an artistic fashion. Very lightly dab the edges of the sheet of pasta with water and then carefully lay a second sheet of pasta dough on top of the herbs, enclosing them between the two sheets of dough. Using your hands, lightly press the two sheets together so that they stick.
Turn the stand mixer speed to level 2. Pass the pasta sheet through the rollers on setting 3 to seal the two sheets together. Repeat the layering and rolling process with the remaining sheets of dough.