Peel the white asparagus and trim off the woody ends. Bring 1 liter of water to a boil with roughly a pinch of salt, a pinch of sugar, and half a lemon. Add the asparagus and cook on medium-high heat for 7-10 minutes until tender.
Wash the small new potatoes and cook them in a separate pot of boiling lightly salted water on medium heat for 15 minutes until tender.
Make the hollandaise sauce: Set a heatproof metal bowl over a pot of gently simmering water on medium heat, making sure the bottom of the bowl doesn't touch the water. Whisk egg yolks and white wine together in the bowl for 2-3 minutes until thick and pale. Slowly add softened butter, one spoonful at a time, whisking constantly and waiting for each addition to combine fully before adding the next. Season with salt, pepper, and lemon juice to taste.
Arrange the cooked asparagus, potatoes, and ham slices on serving plates and pour the hollandaise sauce over them. Garnish with parsley and serve immediately.