Peel and grate the potato into a clean tea-towel and squeeze any excess water out. Place the potato into a bowl, season, add the egg yolk and mix well. Divide into 4 and then shape into a rösti (flat circular shape approx. 15 cm in diameter).
Place a non-stick frying pan over a medium heat add the oil. Carefully place the rösti in the pan and cook for 4-5 minutes before turning them over. The rösti should be golden and crisp before turning.
While the rösti is cooking, heat a large pan filled with about 3 inches of water and the vinegar ready to poach the eggs. The water should be barely simmering.
For the Hollandaise,
Use a microwave to melt the butter, ensuring that the butter is hot.
Place the eggs yolks and vinegar in a bowl and while whisking, gradually add the melted butter and lemon juice to the mixture.
Cook the asparagus in a small saucepan of water for 3 minutes.
Crack the eggs into the water with the vinegar and poach for 3-4 minutes for a runny yolk.
To assemble, place the golden, crispy rösti on the plate, add the asparagus, followed by the poached egg and finally drizzle over the hollandaise sauce.