Pierce the eggs, place them in plenty of boiling water and boil them for about 8 minutes until they are soft and waxy. In the meantime, peel and finely dice the shallot for the sauce. Wash parsley, dab dry and chop except for a little bit for garnishing. Heat the fat in a saucepan and sauté the diced shallots in it. Dust with flour, sweat briefly and add stock and milk while stirring. Bring to the boil, add frozen peas and simmer for about 5 minutes.
Stir occasionally. In the meantime, put the puree powder into a large cup or small bowl and pour 180 ml of boiling water over it. Stir immediately with a fork or spoon and let it stand for 2-3 minutes. Rinse the eggs under cold water, peel and possibly halve them. Stir the parsley, except for something to sprinkle, into the sauce and season to taste with salt and pepper. Arrange eggs, parsley sauce and mashed potatoes on a plate and sprinkle with the rest of the parsley.