In a medium saucepan, place potatoes and enough water to cover. Bring to boiling; reduce heat. Simmer, covered, for 20 to 25 minutes or till just tender. Drain well; cool slightly. Peel the potatoes. Cover and chill for 4 to 24 hours.
Using the coarse side of a hand shredder, shred the potatoes. (Or, use the shredding blade of a food processor to shred the chilled potatoes.) In a large bowl, combine shredded potatoes, onion, cheese and salt.
In a very large nonstick skillet, heat butter over medium heat till melted (or, heat oil over medium heat). Evenly spread potato mixture on bottom of skillet. Use a large spoon or spatula to press mixture down into a solid cake so it will stick together. Cook, uncovered, for 15 minutes, shaking pan occasionally to loosen the potato cake from bottom of skillet.
Place a large plate upside down on top of the skillet and carefully invert the skillet so the potato cake falls out onto the plate. Slide the inverted potato cake back into the skillet. Cook for 8 to 10 minutes more or till very crisp and golden brown. Slide potato cake onto serving platter. Cut into wedges. Season to taste. Serve with any type of meat or vegetable.