Start by steaming some baby potatoes until perfectly tender.
While the potatoes are steaming, cut the bottom ends off the asparagus, peel them (but avoid the tender tips) and boil them, either in a skillet or in a asparagus cooker filled to an inch or two with water, for 5-10 minutes, depending on how thick they are and how crisp you like them.
When both the asparagus and potatoes are just about the way you like them, make the hollandaise sauce by placing two or three egg yolks in a bowl that is sitting above a pot of simmering water, add the juice of half a lemon and a bit of salt and whisk briskly until the eggs are quite frothy. As they heat up, they will begin to thicken.
Ddd a 1/2 cup of butter, which you will have melted separately, bit by bit, as you continue to whisk. As each bit of melted butter is absorbed by the egg, add a bit more butter, whisking all the time, until you have a nice creamy sauce. Add hot water to thin out the sauce if need be and remove from the heat.
Transfer the asparagus and potatoes to a serving dish (making sure they are well drained) and pour over the hollandaise sauce.
Sprinkle some finely chopped parsley over the dish and serve immediately.