Cut each potato lengthwise into 1/4-inch-thick disks, then cut these disks lengthwise into 1/4-inch-thick sticks. Try to keep your cuts uniform so the potatoes cook evenly.
Soak the potato sticks in cold water for 20 minutes. Drain and rinse the potatoes in 3 changes of fresh cold water, draining after each rinse. Let the potatoes dry in a single layer on a towel-lined baking sheet.
Meanwhile, heat the oil in a pot that holds at least 6 quarts over medium heat until it reaches 330°F on a deep-fry thermometer.
Blot the potatoes completely dry with more towels. Gently drop one-third of the potatoes into the oil and increase the heat to medium high (the oil temperature will drop to about 300°F and then gradually rise—it’s fine if it doesn’t return to 330°F). Cook, stirring occasionally with a skimmer or a large slotted spoon, until the potatoes soften (you should be able to cut them with the side of the spoon) and are slightly blistered and creamier in color (remove them if they start to brown), 2 to 3 minutes.
Scoop out the potatoes, shaking them to drain off excess oil, and transfer to a baking sheet lined with paper towels, arranging them in a single layer. Fry the remaining 2 batches of potatoes in the same manner, letting the oil return to 330°F before each batch.
Heat the oil until it reaches 360°F. Add one-third of the potatoes and cook, stirring, until they turn golden-brown and become crisp (to test, carefully drain one on paper towels and try it), 1 to 2 minutes. Transfer the fries to a baking sheet lined with fresh paper towels and sprinkle generously with salt. Fold the edges of the paper towels up and over the fries (to make a little pouch) and shake well so the salt is evenly distributed. Serve the fries immediately. Fry the remaining 2 batches of fries in the same manner, letting the oil return to 360°F before each batch.
You can cut, soak, and do the first fry on the potatoes up to 2 hours ahead. Keep at room temperature and do the second fry just before serving.
Fresh, hot French fries pair well with so much more than plain ketchup. For a twist, try one of these suggestions: