Grate potatoes into a plate or bowl so they are ready to cook once the pan is heated. Use the large holes of a grater.
Preheat a large pan over medium heat, then melt butter into the pan until the butter starts to foam. Once the foaming subsides, place the grated potato in the pan. Roughly half a medium potato should be large enough for a single serving, but also small enough to ensure it cooks evenly. Lightly salt the potato once it's grated into the pan.
Cook until one side is crispy and golden, then flip over. Lightly salt the freshly cooked side.
Leave the flipped hash brown in the pan until both sides are golden and the centre is softly cooked through.
Remove the hash brown from the pan and repeat as necessary.