First, slice the potatoes lengthwise into quarter- to half-inch thick ovals. Then, place one potato slice flat on the cutting board in front of you and position the 2 wooden skewers against the long sides of the potato. Carefully make diagonal cuts in the potato, spaced about a quarter-inch apart, using the skewers as guides to help you only cut partway through the potato. Then, flip the potato over, reposition the skewers on the long sides again, and make diagonal cuts in the opposite direction.
Repeat until you've cut all the potatoes into their accordion shape.
Next, fill a deep frying pan with about an eighth- to a quarter-inch of vegetable oil and heat over medium-high. Once the oil is very hot, add the potatoes in a single layer (you will likely have to work in batches). Season with salt and pepper, and fry until the bottoms of the potatoes are golden brown and crispy, about 6 to 8 minutes. Flip and continue frying until the other sides are crisped, about 2 to 3 minutes.
Transfer fried accordion potatoes to a plate lined with paper towels to allow the excess oil to drain off. Serve immediately.