Parboil potatoes the night before. Bring a pot of water to a boil and add potatoes in. Boil for about 8-10 minutes until the outer part of the potato is just tender (but not soft) and the inside is still raw and crunchy. If you insert a chopstick into the potato, it should be able to penetrate the potato but meet with resistance nearing the middle.
Note: don't overcook the potatoes otherwise they will be hard to grate.
Remove the potatoes and cool in an ice water bath, then peel the potato skins using a knife or peeler. Keep potatoes in the refrigerator for a few hours, best overnight. This is to ensure that the potatoes are firm enough to grate. Grate potatoes using a food processor or shredder.
Add melted butter, salt and pepper to potato shreds and mix evenly.
Heat a 20cm or 24cm frypan over medium heat and add 1 tbsp of oil. Allow oil to heat up till hot before adding shredded potatoes in. Fry for 3-4 minutes until underside turns brown and crispy. Flip rösti onto a plate.
Add ½ tbsp of oil into pan, then slide rösti back into the frypan. Fry for another 3-4 minutes until crispy and brown. Remove rösti from pan. Serve rösti with greek yoghurt.