Peel and quarter the potatoes, peel and dice the carrots, wash the leek and cut into rings. Boil the potatoes in salted water for 20 minutes. Add the carrots and leek to the potatoes about 10 minutes before the end of the cooking time.
Boil eggs (about 10 minutes, egg yolks must be firm). Melt the fat in a saucepan, sweat the flour until golden, deglaze with the stock and milk, bring to the boil and stir in the mustard. Season to taste with salt and pepper.
Peel and halve the eggs. Drain the potatoes and vegetables and carefully add to the sauce.
Arrange in a deep bowl and spread the eggs on top.