Put the potatoes in a medium bowl, then add the egg, salt and cheese.
Mix until thoroughly combined. In a griddle or frying pan over medium heat, add the butter. When it’s melted, measure ¼ cup of the potato mixture and drop onto the pan or griddle.
Using your spatula, flatten the mixture down into a pancake about ½-inch thick. Fry until the pancake is golden brown (roughly 5 minutes for each side).