One day in advance: Boil the potatoes in a large pan of salted water. Drain, cool and keep covered in the refrigerator.
To prepare: Grate the potatoes and season with salt. Mix in the grated cheese. Form the mix into bite sized balls.
Heat the butter and oil in a frying pan. Use a spatula to flatten the potato mix. Fry for 10 minutes until a crisp brown crust has formed on the bottom. Flip the rostis, and fry the other side brown and crusty.
Set aside in a warm oven until ready to serve.
Oil a frying pan and place over a medium heat.
Using a knife, carefully crack the quails' eggs into ramekins or small cups: each egg should have its own container.
Pour the eggs into the hot pan, and leave to fry until the white is just barely set.
Season with salt and pepper, and place an egg on each rosti. Serve immediately.
«For larger parties, the rostis can cooked in advance, then re-heated and crisped up at the last mnute.»