These are not at all like the frozen pre-fried chopped and compressed patties you find in fast food establishments for breakfast or in your grocer's freezer case. They are the shredded style, made with the homemade touch.
This recipe serves 4 people as a side, or two people if they are hungry.
Scrub potatoes and peel them if the skins are thick. If you choose to peel them, weigh after peeling. Shred on the coarse disk of a food processor, or if you don't have one, use the coarsest hand grater you can find. Do not put them in the food processor to chop with the blade, as you need shreds for this recipe.
Put the potatoes in a bowl. Sprinkle over the salt and mix well. Leave for 1/2 hour to draw off the water. Then put in a strainer and rinse well with cold water. Drain and squeeze well to get them as dry as possible. Add the rice flour and the potato starch to the potatoes and mix until they are coated and there is no loose flour.
Heat half the butter and oil in a 12" frying pan until the butter is melted. Scatter over the potatoes, arrange them with a fork so the layer is even, then tamp down with the fork. Heat over medium heat until the potatoes are brown on the bottom when you peek. Slide the potatoes onto a dinner plate. Place another plate on top, then flip so that the browned side is on top. Put the remaining butter and oil in the frying pan, swirl to coat, and slip the potatoes back in. Lower the heat to medium-low and cook until browned on the bottom. Cut in quarters with a spatula. Sprinkle with freshly ground pepper when serving.
These can be topped with fried onions, crisp bacon, ham, peppers, or melted cheese. You can make them in two 10" pans, put filling in them, and fold them over like an omelet.