Peel the potatoes, leaving a patch of skin at both ends. Cut lengthwise into 1/4-inch-thick slabs, then cut the slabs into 1/4-inch-wide sticks. (Or use a mandoline for faster-to-cut fries.) Soak the potatoes in a bowl of icy water, 15 minutes. Drain and dry on a thick kitchen towel or layers of paper towels.
Fill a countertop fryer with oil or pour 3 inches of oil into a large Dutch oven. Heat the oil to 275ºF. Fry the potato sticks in small batches for about 6 minutes, then remove and drain on cooling racks. Increase the oil temp to 375ºF. Refry the fries in small batches until they are as brown as you like, drain on paper towels and season with sea salt.