Pulse the onion in a food processor a few times until the onion is diced into crunchy bits. Remove the blade and scrape the onion into a small bowl. Return the food processor bowl to the machine. (Don't wash it yet.).
Cut the potatoes lengthwise to fit in the food processor feed tube. Put the medium-coarse food processor shredding disk and turn it on. Begin feeding the potato slices into the machine.
When the potatoes are shredded, put them in a colander over a large bowl. Dump in the onion bits and mix everything around with your hands, squeezing the potato moisture out as you work. Let the mixture drip for a few minutes.
Pour out the potato liquid from the bowl, but leave the starch that clings to the bowl. Dump in the shredded potato and onion mix. Add the eggs, matzoh meal, parsley, salt, and pepper. Stir well. Then let it sit for about 10 minutes.
In a large cast-iron skillet, pour in ¼ inch of oil. Over high heat, get the oil very hot. Using a ¼-cup measure or a long-handled serving spoon, spoon the batter into the skillet. Flatten each with a metal spatula to a diameter of 4 to 5 inches. Don't worry about them being uniformly round. Reduce the heat to medium and cook the latkes until golden brown on one side. Then turn over and fry them some more. When crispy on the outside and moist inside, about 5 minutes per side, remove and place on several thicknesses of paper towels. Keep doing this until you run out of batter.
Serve the latkes immediately.