Preheat oven to 250 and set a cooling rack into a rimmed baking sheet.
Fill a large bowl with cold water and set aside. Peel potatoes and grate with a box grater on the largest hole - you want these coarsely shredded. Transfer the shredded potato to the bowl of cold water as you go. Soak the shredded potatoes for about 2 minutes after the last batch is added to the water, then drain well in a colander.
Spread the shredded potato and chopped onion on a clean kitchen towel. Roll the towel up tightly and twist to wring out as much liquid as possible. Transfer the potato mixture to a large bowl and stir in the egg and salt.
In a large, deep sauté pan, heat about 1/4" of oil over medium-high heat. Working in batches of 4, spoon about 2 tablespoons of batter per latke into the hot oil. Use the back of your spoon to flatten the latkes. Cook until the undersides are golden brown and crisp, about 3 1/2 minutes. Gently turn the latkes over and continue cooking for another 3-4 minutes, until other side is golden brown. Use a slotted spatula to transfer the latkes to a paper-towel lined plate to drain. Sprinkle with kosher salt.
Add more oil to the skillet as needed and maintain the oil at 350 degrees. Repeat with remaining potato mixture. Keep the latkes warm by transferring them to prepared baking sheet in oven.
Serve hot with sour cream and applesauce.