This is an exceedingly nice dish to serve in the Fall when chestnuts are fresh. Shell chestnuts, blanch them, then boil them until tender; drain and press through a colander. Add hot milk, butter, salt and pepper. Beat until light and stand over a kettle of hot water while you poach the eggs. Dish the chestnut puree in a small platter, cover the poached eggs over the top, dust them with salt, pepper and chopped parsley.