Peel and wash the potatoes, halve or quarter them depending on size and cook in boiling salted water for about 20 minutes
Pierce the eggs, place in boiling water and cook for about 9 minutes. Then drain, rinse well and remove the shell
Meanwhile melt the fat in a pot, dust with flour, sweat on and gradually deglaze with broth and cream while stirring constantly, bring to the boil. Stir in mustard. Season to taste with salt, pepper and sugar. Keep warm. Wash parsley, shake dry and chop finely
Add eggs to the mustard sauce. Drain the potatoes, let them steam briefly and sprinkle with parsley. Arrange mustard and parsley potatoes on plates