Put the peeled asparagus in boiling salted water with sugar and 1 teaspoon butter. Cook for about 20-25 minutes, drain and keep warm.
Heat the remaining butter in a saucepan. Sweat the flour in it while stirring. Deglaze with the milk and simmer for 15 minutes. Add the processed cheese in flakes and stir until it has dissolved. Alloy with the egg yolk. Take the sauce off the stove. Season to taste with salt, pepper and nutmeg.
Arrange asparagus stalks, pour the sauce over them, garnish with egg slices and parsley.