Beat the eggs in a mixing bowl, then add the flour bit by bit, whisking all the time until you have a rather thick uniform paste. As you continue whisking, drizzle in enough water that the batter attains the consistency of light cream. Whisk in a pinch of salt and, if using, the parsley and/or nutmeg.
Let the batter rest for a good 30 minutes or more at room temperature.
Heat the oil (or lard) in a crepe pan or small nonstick skillet (about 23cm/9 in diameter). When the pan is hot, drizzle in a bit of oil (or melt a small knob of lard) and then pour on a small ladleful of the batter and swirl it around so it very thinly covers the bottom of the pan. Let the batter set, and when it just begins to brown on the bottom, flip it over and let it cook very briefly on the other side. The whole operation should take less than one minute. Remove the resulting crêpe aka scrippella to a dish.
Repeat until you've used up all the batter.
Bring your broth to a simmer.
Lay your scrippelle aka crepes out on a flat surface to dry a bit, then top each with a very generous portion of the grated cheese. Roll the crepes up very tightly, with the prettier side on outside, and arrange them, in soup plates, seam side down.
Ladle the piping hot broth on top of the crepes.
Serve right away with more grated cheese on the side for those who want it.