Wash the potatoes thoroughly. Boil up in a pot covered with water. Cook for about 20 minutes. Wash and peel the asparagus, cut off the lower woody ends. Put asparagus in lightly salted boiling water with a little sugar, bring to the boil and cook for about 18 minutes.
In the meantime, drain the potatoes, rinse and peel them. If necessary, cut the potatoes in half. Peel onion and chop finely. Wash basil, dab dry and cut into very fine strips.
If necessary, puree with 2-3 tablespoons of asparagus water. Heat the oil in a pan and fry the potatoes until golden brown, turning them over. Season with salt and pepper. In the meantime, pour the asparagus into a sieve, collecting the asparagus water.
Measure 350 ml asparagus water. Keep asparagus warm. Melt the fat in a pot, fry the onion in it until transparent, dust with flour, sweat it and gradually deglaze it with measured asparagus water and milk while stirring.
Bring to the boil and season with salt, pepper and sugar. Remove from the stove. Whisk the egg yolks and 3 tablespoons of sauce, stir into the sauce. Stir basil into the sauce. Arrange asparagus with sauce, potatoes, salmon ham and cooked ham on a plate.
Garnish with basil leaves and strips.