Peel, wash and boil the potatoes in salted water. Hard boil the eggs. Peel the shallots and dice them very finely. Pluck the parsley and roughly chop it. Cut the ham into small cubes and drain the capers well.
Fry the shallots in the butter. When they are nice and translucent add the ham and capers. Dust the flour over it and continue to fry everything briefly, stirring constantly. Gradually pour in the milk, stirring well with the whisk so that no lumps form.
When the sauce has a creamy consistency, add the mustard and stir everything well again. Let everything simmer a little longer, then season the sauce with salt, pepper, sugar and lemon juice.
Peel the eggs, add them to the sauce and reheat everything together.
Arrange the eggs with the potatoes and sprinkle everything with the chopped parsley