Peel and wash the potatoes and cook them in boiling salted water for about 20 minutes. Peel, wash and slice carrots. Cook peas and carrots in boiling salted water for about 5 minutes.
In the meantime, boil the eggs in boiling water for about 8 minutes. Melt fat in a pot, stir in flour and sweat it. Deglaze with broth while stirring, stir in milk and mustard, let simmer for about 5 minutes.
Drain the eggs and quench. Season mustard sauce with salt, pepper and sugar. Add vegetables to the sauce. Drain potatoes. Peel and quarter eggs. Arrange eggs with pea-carrot-mustard sauce and potatoes.
Garnish with chervil.