At least 12 hours before frying, heat oven to 350°F and position a rack in top half of the oven. Set an empty sheet pan on a lower rack.
Using a dinner fork or paring knife, poke several holes in the potatoes to allow water vapor to escape during cooking. Coat each potato lightly with 2 teaspoons of the peanut oil and sprinkle generously with salt.
Bake the potatoes directly on the oven rack until tender and an instant-read thermometer inserted into the center of a potato reads between 185°F and 195°F, 45 minutes to 1 hour.
Cool to room temperature and then refrigerate overnight, unwrapped if possible
The next day, heat the 2 quarts peanut oil over medium-high heat to 375°F in a large Dutch oven fitted with a deep-fry thermometer. (As the temperature crosses 350°F, turn down the heat to medium so that you don't shoot through the target temp.) Line a rimmed baking sheet with paper towels, then place a wire cooling rack upside down on the paper towels.
Meanwhile, slice the cold potatoes into half-inch-thick batons, leaving the skin attached. Boost the heat back to medium-high slightly before adding the first fries and cook 8 to 10 at a time until golden brown and delicious, 2 to 3 minutes. (You may have to adjust the heat to maintain the oil temperature, so keep an eye on it.) Use a spider to fish the fries from the oil to the prepared rack. Sprinkle with additional salt while hot and devour.