Preheat the oven to 450 degrees F. Spray a baking sheet with cooking spray.
Cut each of the potatoes in half lengthwise. Rest each half on its flat side and cut each half lengthwise, straight down into 4 even slices. You will have 16 slices altogether. Cut the rounded edge off of the outermost slices so each slice can lay completely flat on either side. Put the potatoes into a medium bowl and toss with the oil.
Place the potatoes on a baking tray and bake for 20 minutes. Sprinkle the potatoes with cheese on their up-facing side and continue to bake for another 15 to 20 minutes, until they are crisp and golden brown. There is no need to turn them. Season with salt and serve immediately.