Choose whether to peel the potatoes. If leaving the skin on, scrub thoroughly and check under a small patch for green coloring. If peeling, use a vegetable peeler to remove all skin.

Cut a flat side on each potato for stability, then lay flat side down on a cutting board. Slice potatoes a bit thicker than 1/4 inch, then cut those slices into long sticks. Place each fry into a bowl of cool water to stop browning as you're working.

Rinse the cut potatoes in a colander for about a minute. Soak them in cool water for 10 minutes, then drain, rinse again, and dry the fries thoroughly with a kitchen towel.

In a heavy-bottomed saucepan at least 8 inches wide, or a deep fryer, add enough beef tallow or duck fat to reach a few inches up the sides. Heat it to 325°F (165°C), checking with a thermometer. Fry about half the potatoes for 5 minutes, stirring occasionally, then transfer to a plate lined with paper towels. Let the fries rest for 5 minutes.

Raise the fat's temperature to 375°F (190°C). Fry the partially cooked potatoes for an additional 3 minutes, stirring often, until golden brown. Transfer to a large paper towel-lined mixing bowl to drain briefly.

While fries are still hot, sprinkle with salt and toss to coat. Serve immediately with your favorite dipping sauces or enjoy them plain.