Peel, wash and halve the potatoes and boil them in salted water for about 20 minutes. Peel and finely chop the onion. Heat the oil in a coated pan and sauté the onion. Add stock and 125 ml milk, bring to the boil.
Stir in the mustard. Add the sauce thickener while stirring and simmer for about 2 minutes. Bring approx. 1 litre of salt water and vinegar to the boil. Beat the eggs one by one in a ladle and carefully slide them into the vinegar water.
Cook over low heat for 5-6 minutes. Remove with a skimmer, drain and keep warm. Drain the potatoes and mash them coarsely. Add 125 ml milk. Season with salt and nutmeg and mash to mashed potatoes.
Wash the chives, dab dry, chop finely and fold into the purée. Arrange mashed potatoes, poached eggs and mustard sauce on plates. Serve garnished with tomato wedges, lettuce leaf, chives and parsley.