Peel and slice the potatoes, then shred them using a food processor fitted with the grater attachment. Place shredded potatoes in a cheesecloth and squeeze out as much moisture as possible.
Measure 2 cups of the drained shredded potatoes into a medium bowl, reserving any extra for another use. Add the egg, flour, onion, and salt, stirring until well combined.
Heat 1/4 inch of oil in a large, heavy-bottomed skillet over medium-high heat. Scoop large spoonfuls of the potato mixture into the hot oil, pressing down to form patties about 1/4 to 1/2 inch thick. Cook until golden brown, 4–5 minutes per side.
Remove the cooked latkes to a paper towel-lined plate to drain excess oil. Repeat with remaining mixture. Serve immediately while hot.