Coarsely grate the potatoes on a box grater or in a food processor. Sprinkle with salt, toss lightly, and transfer to a fine-mesh strainer over a bowl. Let sit for 10 minutes.
Using a wooden spoon or spatula, press as much water out of the potatoes as you can and transfer to a bowl. Sprinkle with the Parmesan and toss lightly with a fork.
Heat a large cast-iron or stainless steel skillet over medium-high heat until hot. Add the olive oil, and then add the potatoes in an even layer. Allow to cook without stirring for several minutes. Using a spatula, check that the bottom is browned. When golden brown, flip and continue cooking until the other side is well browned.