Wash and peel the potato. Slice the potato into thin slices. Alternatively, grate the potato. Place the grated potato in a cheesecloth and squeeze until the grated potato are dry.
Heat oil in frying pan. Add in the sliced/grated potato and stir it around until they are coated with oil evenly. Season with salt and plenty of black pepper.
Spread the potato in a single layer and let it fry, untouched for several minutes, until the undersides of the potato turns golden-brown in colour. Flip to the other side and let it fry until it turns golden-brown.
Crack the egg in the middle of the rösti (break the egg if you want to) and spread the egg white around the rösti. Once the egg is set on the underside, flip the rösti and let the egg set.
Serve immediately.
NOTES
The key is to not touch the potato while it's frying so that it can acquire the golden-brown crust