Grate the potato into a bowl lined with a tea towel.
Squeeze the tea towel to remove excess liquid and season the potato with salt.
Heat the butter and oil in a pan, add the potato, and press down.
Fry for 4-5 minutes per side until crisp and golden.
Cut the rosti into wedges and place on a plate.
Simmer water and vinegar in a saucepan and create a whirlpool with a spoon.
Crack an egg into the whirlpool and cook for 3-5 minutes until set.
Remove with a slotted spoon and repeat with the second egg.
Serve the poached eggs on top of the potato wedges.