Whisk eggs and milk, season with salt, pepper and nutmeg. Pour the egg milk into a greased, flat form, cover and leave to stand in a hot water bath for 30-40 minutes. In the meantime, peel and finely dice the onion.
Clean, wash, peel and cut the carrots into fine strips. Heat the oil in a pot, fry the onion in it until transparent, add the carrots and fry. Deglaze the vegetables with the vegetable stock, bring to the boil and season again with salt and pepper.
Turn out the eggs from the mould, cut into rhombuses and add to the stock. Wash parsley, dab dry and chop finely. Arrange soup in deep plates and serve sprinkled with parsley.