Peel the potatoes, immediately immersing them in very cold water as you finish each one.
Remove the potatoes from the water. Grate the potatoes and onion with a food processor fitted with the grating blade. Don't press too hard on the potatoes going in -- just enough to get them through.
Transfer the potatoes and onion to a fine-mesh strainer; squeeze out all the water into a bowl. Let the potato starch settle, then pour out as much water as possible, leaving the starch in the bowl. Add the potato-onion mixture to the bowl and mix in the egg, flour, 1 teaspoon salt, and pepper to taste.
Heat a well-seasoned cast-iron skillet with a thin layer of vegetable oil over medium heat. Scoop large spoonfuls of the potato mixture into the pan and flatten them out (thin pancakes yield crispy ones). Fry until golden on the bottom, then gently flip and fry the other side, 3 to 4 minutes per side. Drain on paper towels. (If you have to wait to serve, re-crisp them on a baking sheet lined with clean paper towels in a 350 degrees F oven.)
Serve with applesauce, or try my family's favorite toppings: My great-grandmother put cinnamon in applesauce to serve with hers. My grandfather loved his with heaps of cold sour cream. My grandmother served them with poached pears. My mother tops them with tart, chunky homemade applesauce. My brother, Willie, loves his plain with sugar. My stepfather, Ronnie, loves his with ketchup -- but I wouldn't brag about that!