Peel potatoes and coarsely grate them. Rinse them in a strainer with cold water. Then using a potato ricer compress the water from the potatoes (do not force potatoes through). You may also wring the potatoes in a cloth towel and then pat them dry.
In a two-quart bowl, combine the potatoes, onions, and salt and pepper (if using cheese add now). Toss the potatoes to evenly distribute the ingredients .
In a ten-inch frying pan (nonstick works best), melt the butter over medium-high heat. When it is bubbly, add the potatoes and reduce the heat to medium low. Press the potatoes evenly with a large spatula. They should be no more than a half-inch thick. Cook for ten minutes. Then with a spatula, cut the hash browns evenly in to four wedges for easy turning. Turn them over and cook the other side for another seven or eight minutes until the potatoes are tender. Serve hot.