Generously cover potatoes with cold water in a 3-to 4-quart pot and add 1 tablespoon salt. Boil until almost tender, 10 to 15 minutes. Drain potatoes. Transfer to a baking sheet and lightly crush to about 3/4 inch thick with a potato masher, keeping potatoes intact as much as possible.

Heat oil in a 12-inch heavy skillet over medium-high heat until it shimmers. Transfer potatoes with a spatula to skillet, then lower heat to medium-low and cook, turning once, until golden brown, about 20 minutes total. Serve sprinkled with cheese. Season generously with pepper.