Peel and rinse the potatoes, then cut them into sticks by cutting each potato into 4 or 5 vertical pieces, then cutting each piece into sticks. Put the potato sticks in a large bowl, cover with cold water and swish them around to get off the extra starch. Pour off the starchy water and add fresh water. Continue washing the potatoes until the water runs clear. Cover with water again and allow them to soak for 2 or 3 hours. (You can also stick them in the fridge and let them soak for up to 3 days.)
When you're ready to make the fries, drain off the water and lay the potatoes sticks on baking sheets lined with paper towels. Blot them with more paper towels to dry them.
Heat a few inches of oil in a heavy pot until a deep-fry thermometer registers 300 degrees F. In 3 or 4 batches, cook the potatoes until soft, about 1 minute per batch. They should not be brown at all at this point! You just want to start the cooking process. Remove each batch and drain them on new/dry paper towels.
When all the potatoes have been fried once, turn up the heat until the oil reaches 400 degrees F. Start frying the potatoes in batches again, cooking until the fries are golden and crisp, 1 to 2 minutes. Remove from the oil and drain on paper towels.
Sprinkle the fries with sea salt and dive in!