Place the flour in a large bowl; make a hole in the middle and add the eggs, the water and a big pinch of salt salt.
Start incorporating the eggs and water going from the inside out, then start kneading until it forms a mass.
Transfer dough to a lightly floured board and knead for 8 minutes. Add the oil and knead for 1 more minute.
Wrap in plastic, and let rest for 40 minutes at room temperature before rolling with a rolling pin or a manual pasta machine on the widest setting.
Cut the dough into 8 pieces: run each piece through the machine, then fold in half and do it again, moving to narrower settings after 2 passes and continuing to dust with flour to prevent sticking, until pasta sheet is nice and thin. If rolling with the rolling pin, keep folding the pieces in half and re-rolling, adding flour to prevent the dough from sticking, till the pasta is thin enough.
Variations - Make colored pasta
Red/Orange: add a tablespoon or two of tomato paste diluted in one tablespoon water to the dough.
Green: Steam or microwave 1⁄2 lb. spinach (or 1⁄4 lb. frozen spinach) until soft, squeeze the water out, process in a blender or food processor until very fine and add to the dough. If too wet, add a little flour.
Brown: Add 1 tablespoon unsweetened cocoa.
Speckled herb pasta: Add about 5 tablespoons finely chopped fresh herbs (mix basil, mint, sage, parsley, etc.).
Fancy: If you roll the pasta super- thin with the machine, you can place a few basil leaves or organic rose petals between two sheets after brushing the sheets with little water and egg white as needed.
Yellow: Add 1⁄2 teaspoon ground saffron or turmeric diluted in 1 or 2 teaspoons warm water.
Pink/Purple: Add 1 or 2 cooked beets, processed.