Melt the butter slowly in a small pot and keep it warm without letting it brown.
Fill a larger pot with a few centimeters of water and bring it to a light simmer.
Whisk the egg yolks with the lemon juice in a metal bowl that fits over the pot without touching the water.
Place the bowl over the steam and whisk the yolks until they start to thicken and turn creamy.
Pour the warm butter into the yolk mixture in a thin stream, whisking all the time so the sauce turns smooth and glossy.
Season the Hollandaise with salt and pepper and take the bowl off the heat so the sauce does not overcook.
Arrange the hot potatoes and asparagus on warm plates and spoon the Hollandaise over the spears.
Finish with chopped dill or parsley and serve right away while everything is still hot.