Peel potatoes with peeler. Grate coarse using box grater into bowl. Grate onion same way. Bundle shreds in cheesecloth over sink. Squeeze hard with hands till barely moist, wring twice.
Dump squeezed potatoes onions back in bowl. Add melted butter, salt, pepper from measuring spoons. Toss even with hands till coated sticky.
Heat 2 tbsp butter in skillet over medium using measuring spoon till foaming. Pack half potato mix into ½-inch thick patty using spatula edges. Fry 10 minutes till bottom deep gold crispy.
Loosen edges gentle with spatula. Flip careful onto plate then back to skillet. Add rest butter around. Fry second side 10 minutes golden. Press flat midway with spatula for even crisp.
Slide rösti onto board. Rest 2 minutes. Cut wedges with knife. Fry second batch same way if needed.
