Peel the potatoes and cover with cold water until you are ready to make the pancakes.
Grate the potatoes and onion into a strainer that is suspended over a bowl to catch the juices. If this is hard to manage, grate the potatoes into a bowl, then turn into a strainer suspended over another bowl. Grate the potatoes and onion alternately, as the onion juice will help prevent the potatoes from darkening.
Using a wooden spoon, or picking up handfuls of the grated potato mixture, squeeze or press out as much liquid as possible over the bowl. Reserve all liquid and let it settle in the bowl for two or three minutes
Put the pressed potato and onion mixture in a clean bowl. Carefully pour off the watery part of the reserved liquid but do not discard the thick, starchy paste at the bottom of the bowl. Scrape that into the potato mixture.
Add the egg yolks, potato flour or matzoh meal, salt, pepper and parsley if you are using it. Mix thoroughly. Beat the egg whites into stiff and shiny peaks and gently fold them into the potato mixture.
Heat a half-inch depth of oil in a heavy skillet, preferably of black cast iron.
Drop the potato mixture into the hot oil, about two tablespoons per pancake, and fry, turning once so the pancakes are a deep golden brown on both sides. Total frying time for each batch of pancakes should be about 10 minutes. Drain on paper towels.
Keep fried pancakes warm while the rest are being fried. To do that, put the fried, drained pancakes on a rack in an open baking pan and place in a low-heated oven (about 250 degrees). Do not hold for more than 15 minutes before serving or they will become soggy.