Scrub the potatoes well under running water, leaving the skins on. Cut the potatoes into long, even sticks, about 1/4 to 1/3 inch thick.

Immediately place the cut fries into a large bowl of cold water. Let them soak for at least 1 to 2 hours. Change the water after 30 minutes. This step is crucial as it removes excess starch, which helps the fries get crispy and prevents them from sticking together.

Drain the potatoes and lay them out in a single layer on a clean kitchen towel or paper towels. Pat them completely dry. Any moisture left on the potatoes will cause the hot oil to splatter dangerously and will result in soggy fries.

Pour the peanut oil into a deep fryer or heavy-bottomed pot until it reaches a depth of 2 to 3 inches. Attach a thermometer to the side of the pot, ensuring the tip is submerged but not touching the bottom of the pot. Heat the oil to 300°F.

Carefully add a handful of thoroughly dried potatoes to the hot oil. Do not overcrowd the pot, as this will lower the oil temperature. Fry for about 5 to 7 minutes until the fries are soft and cooked through, but pale and limp—they should not have any color. Using a spider or slotted spoon, remove the fries from the oil and let them drain on a wire rack or paper towel–lined baking sheet. Continue this process in batches until all the potatoes have been blanched. Let the blanched fries cool at room temperature for at least 30 minutes (or up to a few hours).

Heat the oil to 375°F.

Working in small batches, return the cooled, blanched fries to the hot oil. Fry for 2 to 4 minutes, or until golden brown and crispy on the outside.

Quickly remove the fries from the oil and let them drain for only a few seconds before transferring to a large mixing bowl. Liberally sprinkle the Cajun seasoning over the hot fries and toss vigorously to coat.