Preheat oven to 200°C. Line a baking tray with parchment paper and brush parchment with oil.
Peel potatoes and slice lengthwise into 24 slices, just under 1/4-inch thick (using a mandolin is easiest).
Place 12 potato slices onto prepared baking tray. Arrange a slice of chorizo on each potato slice and sprinkle with cheese, leaving edges of potato clear.
Cover cheese with remaining potato slices. Place a sheet of parchment paper over “wraps” and place a second baking tray on top.
Bake for 15 minutes, then remove top baking tray and parchment paper and bake until potatoes are golden brown, about 8 minutes more.
Serve “wraps” warm or at room temperature.