Wash, peel and cut the potatoes into pieces. Cook in boiling salted water for about 20 minutes. Melt 25 g fat in a pot. Sprinkle flour over it and sweat while stirring. Deglaze with 300 ml water and cream and bring to the boil.
Stir in the stock, let it simmer at low heat for about 10 minutes, stirring frequently. Cook eggs in boiling water for about 7 minutes. Heat milk and 25 g butter. Wash chives, dab dry and cut into rings.
Drain the potatoes and let them evaporate briefly. Add milk mixture and mash everything to a puree. Season to taste with salt and nutmeg. Drain eggs, rinse with cold water and peel. Flavour sauce with mustard, salt and pepper.
Arrange eggs with mustard sauce and mashed potatoes. Sprinkle with chives.