Heat the oil on a large, flat cast iron griddle or skillet over medium-high heat. Immediately "scatter" the potatoes over the oil. Season with salt, to taste. "Scatter" over the onions and cook, without stirring, until the outermost edges have started to brown, about 2 1/2 minutes. Flip the hash browns with a spatula, and place the cheese on top. Let the cheese melt, about 30 seconds.
Transfer the hash browns to a plate and serve immediately.