Grate the potato on the coarse side of a box grater. Toss immediately with the salt, then cover and leave for 10-15 minutes until the potato has released its moisture.
Transfer the grated potato to a clean tea towel or muslin cloth. Gather the edges together and squeeze as firmly as possible until no more liquid comes out.
Tip the potato into a bowl and sprinkle over the potato starch. Toss thoroughly so the starch coats the strands evenly.
Heat the oil in a 20cm frying pan over a medium heat. Add the potato mixture, spreading it into an even round. Press gently with a spatula to level the surface, but don’t compact it too firmly.
Cook for 8-10 minutes, adjusting the heat as needed, until the underside is deeply golden and crisp.
Slide the rösti onto a plate, place the pan upside down over the top, then invert everything together so the uncooked side drops neatly back into the pan.
Add the butter around the edges and let it foam. Tilt the pan and baste the rösti continuously with the foaming butter as it finishes cooking for another 6-8 minutes, until both sides are deeply golden and crisp.
Transfer the rösti to a cooling rack for 1-2 minutes before serving. Finish with black pepper and serve immediately.
