Wash and peel the potatoes, and with a French-fry cutter or a kitchen knife, cut them into long strips with a square cross section about 3/8-inch on a side. Wash them briefly under cold water and dry with a cloth. Put them into a pan about 10 inches in diameter with sides at least 4 inches high. Just cover with peanut oil.
Place the pan over the highest heat. When the oil has exceeded 200 degrees, it will begin to bubble, first softly and then furiously, and by the time it reaches 350 degrees, the potatoes will be a deep golden brown and ready to eat. (Make sure the temperature never exceeds 370 degrees.)
Taste one or two. Drain and blot with paper towels. Salt the frites just before serving. Eat with strong Dijon mustard.