Peel the potatoes and, using a cheese grater, shred them directly into a large bowl of cold or chilled water. Peel and grate the onion in the same way, straight into the bowl. Let this sit for 20 minutes. Meanwhile, place the eggs and flour into a large mixing bowl, add in 1 teaspoon of salt, ½ teaspoon of freshly ground black pepper and a pinch of cayenne. Whisk this together until completely smooth then set to one side.
Drain the potato-onion mixture through a colander, pressing down on the mixture to squeeze out as much water as possible. Take one handful of the mixture at a time from the colander, and squeeze as hard as possible to extract the maximum amount of water, then spread the "dry" potatoes on several layers of paper kitchen towels.
Repeat until all the potato mixture has been squeezed dry and then spread onto kitchen paper. Press down on them with some more kitchen towels to get any remaining moisture out then remove the paper towels and transfer the potato-onion mixture to the bowl with the egg mixture. Use a spatula to thoroughly combine the egg and the potato.
Pour about ¼" (0.5cm) of vegetable oil into a large, heavy skillet or frying pan (preferably non-stick) and place over medium-high heat. Once the surface of the oil begins to shimmer, spoon about 5 tablespoons (that's about one-third of a cup) of the potato mixture into the pan, shape it into an approximate circle (no need for accuracy) and flatten to about ½" (1cm) thick. In a large frying pan, you can probably make three or four of these patties at a time. Reduce the heat to medium, and fry the potato pancakes for about 5 minutes on each side until they are browned and crispy (don't forget - the potatoes are raw, so don't cook them too quickly otherwise they will be undercooked in the middle).
Remove from the pan and drain on paper towels. Place in a warm oven until all the pancakes are cooked (or use 2 pans!). To serve, top each potato pancake with fried or poached egg and a big glass of fresh juice!