Wash potato and remove any bad spots, grate into a bowl. Mix in the salt and set aside for 5 minutes. Beat egg lightly, then whisk cream and cornmeal. Using your hands, squeeze the moisture out of the grated potato, then add to the egg mixture. Stir in the ham, onion, and a pinch of salt and pepper. Heat the oil in a heavy skillet over medium heat. Add butter, let it melt, and then spoon about ¼ cup of the patty mixture per patty into the skillet. Don’t crowd the patties. Spread and flatten the patties with a fork to a thickness of about ¼-inch. They should be no wider than your spatula. Fry for 3 to 4 minutes per side, flipping only once; they’ll be dark and crusty on the outside. Serve hot. The patties will hold up for a little while in a hot oven, in case you want to serve them all at once.