Wash and parboil the potatoes in salty water for a maximum of 10min (15min for large potatoes) and immediately after place the potatoes in ice water to cool them down.
In the meantime peel and dice the onions.
Peel the potatoes.
Grate the potatoes and mix with the diced onions and season with salt and pepper.
Heat up the frying pan and add butter and oil.
Divide the mixture into 4 or take enough mixture to form your own desired size Roesti.
Place each mixture into a frying pan and form a round 2cm thick Roesti of 15-20cm diameter or smaller if you prefer.
Fry for about 10min.
Turn and place 1 Emmental cheese slice on the Roesti (or more if desired) and fry for another 10min.
Meanwhile fry an egg for each Roesti.
Serve the hot Roesti with the fried egg on top.