Using the large holes on a box grater, shred potatoes. On a clean kitchen towel, place a large handful of shredded potatoes and wring out as much liquid as possible. Remove from towel and add to a large mixing bowl. Squeeze liquid from remaining potatoes in batches as needed.
Sprinkle with tapioca starch and salt. Toss to mix thoroughly. Heat 12-inch skillet on medium heat. Add 1/4 tsp. ghee or oil to skillet, spreading it evenly over the surface with a basting brush.
Using a half-cup measure, scoop up potato mixture and place in the skillet. With a spatula smooth the round into a 3-3 1/2-inch circle about 1/3-inch high. Continue with remaining potato mixture.
Cover and cook for 5 minutes. Turn potato cakes over and cook on that side for 5 minutes, covered. Remove cover, turn cakes over and cook for 2 minutes, uncovered or until spotty, golden brown. Turn again and cook for 2 minutes more, uncovered. Remove to cooling rack. Cakes can be reheated briefly in dry skillet over medium heat if making ahead of time.
Leave it to Japanese scientists to discover the best and least messy way to eat a burger: