Peel the potatoes and place them in a large saucepan. Add enough water to to cover, along with ½ tsp salt. Bring to a boil and simmer until the potatoes are just slightly tender, about 6-7 minutes. Drain off the water and let the potatoes rest until cool enough to handle.
Shred the potatoes using the shredder attachment of a food processor or the large holes of a box grater. Place shredded potatoes in a dish towel or colander and squeeze out as much excess moisture as possible. Season potatoes with remaining salt and pepper. Set aside.
Add olive oil to a heavy-bottomed 10-inch skillet over medium heat. Once the pan is hot and the oil is shimmering, add the potatoes, spreading them out so they form an even layer filling the pan. Cook until the bottom of the potatoes are crisp and deep golden brown, about 12-15 minutes. Place a plate over the skillet and carefully invert it so that the potato cake rests on the plate, crispy side up. Return the skillet to the stove and slide the potato cake back in with the crispy side facing up. Continue cooking until the bottom potatoes are crispy and golden, about 8-10 minutes more.
To serve, transfer to a platter and slice into wedges.
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