Preheat oven to 400° Fahrenheit. Fill large bowl with cold water - add small amounts of ice if needed to keep water cold. Rinse potatoes well under running water, washing away any surface dirt. Peel rinsed potatoes completely and discard of potato skins.
Place peeled potatoes on cutting board. Standing one potato up on its end, slice vertically from one end to the other, dividing potato into long slices, each approximately ¼-inch thick. Do not cut slices larger than ⅜-inch. Repeat until all potatoes have been sliced.
Clear cutting board. Place one slice of potato on cutting board horizontally, so ends point right to left. Position 1 skewer against top side of potato slice, and position 1 skewer against bottom side of potato.
Position knife perpendicular to potato. Place knife against end of potato, then work toward other end of potato, making slices every ⅛-inch. Use skewers as bumpers to catch knife and prevent slicing completely through potato.
Once potato has been cut completely across on one side, carefully turn potato over. Place potato horizontally on cutting board again, with 1 skewer above potato and 1 skewer below potato.
Position knife at slight angle across potato. Again, make cuts across potato from one end to the other, this time cutting diagonally when slicing every ⅛-inch. Use skewers as bumpers to prevent slicing completely through to cutting board.
Keeping potato on cutting board, carefully insert one skewer into one end of potato. Slide skewer completely through center of sliced potato and out other end.
Gently stretch potato around skewer, arranging slices in a spiral, with even spacing between each slice. When satisfied with arrangement, place potato and skewer in large bowl of cold water. Repeat process with remaining potatoes.
Once all potatoes have been sliced, spiraled, and soaked in cold water 5 to 10 minutes, line large plate with paper towels. Carefully remove potatoes from water and place on paper towels to drain.
While potatoes drain, line baking sheet with parchment paper. When potatoes are dry, transfer skewered potatoes to parchment paper. Brush potatoes with olive oil and season with salt and pepper to taste, making sure to brush oil and seasoning between slices of potato when possible. Flip potatoes over and brush with oil, salt, and pepper on other side.
Place baking sheet in preheated oven. Bake potatoes 20 minutes, then remove baking sheet from oven and carefully turn all potato skewers over. Return baking sheet to oven and bake 20 minutes more, or until potatoes are golden brown with crispy edges.
While potatoes bake, prepare chimichurri. Place chopped parsley, garlic, lemon zest, olive oil, salt, and pepper in medium mixing bowl. Whisk well until ingredients are fully combined, then set chimichurri aside until ready to use.
When potatoes are golden and crispy, carefully remove baking sheet from oven. Let potatoes rest 3 to 5 minutes, then serve accordion potatoes warm with chimichurri sauce and proteins of choice.