Add 1 tablespoon of kosher salt to a large pot of boiling water. Add the potatoes, bring back to a boil, lower the heat and simmer for 8 to 10 minutes. Drain the potatoes, place them back in the pot with the lid on, and shake the pot roughly for about 5 seconds. Carefully spoon the potatoes onto a baking rack set over a sheet pan in one layer. Set the potatoes aside to cool and dry for 5 to 10 minutes.
Pour the oil into a large roasting pan, tilt the pan to distribute the oil, and place in the oven for 5 to 7 minutes, until the oil is smoking hot. Transfer the potatoes carefully into the oil, toss them lightly to coat each potato with the hot oil, and spread in one layer. Lower the oven temperature to 350 degrees F. Roast for 45 minutes to 1 hour, turning the potatoes occasionally with tongs, until very browned and crisp on the outside and tender and creamy inside.
Transfer to a serving platter, sprinkle with 1 1/2 to 2 teaspoons sea salt and serve hot.