Heat a medium-sized, heavy frying pan over high heat with enough oil to go most of the way up the sides of the patties. When the oil reaches 350°F to 360°F, or a crumble of potato immediately sizzles and begins to darken in the pan, use a thin spatula to transfer the first patty from the board, lowering it slowly in the oil. Fry until medium brown underneath, 1 to 2 minutes, spooning oil over the top of the patty for even color. Carefully turn it over and fry until the second side of the patty is also nicely browned, another 1 to 2 minutes. Lift out of the oil, shaking excess droplets back into the pan, and transfer to paper towels to drain. Sprinkle immediately with salt. Repeat with remaining patties