Put over the fire in a saucepan the milk and butter, let them come to a boil, then add the bread crumbs and flour. Let it cook, stirring all the time until it is a smooth paste and detaches itself from the sides of the pan, remove from the fire and set it aside to cool. When cold beat the eggs light, stir in a little at a time, beating well until the mixture is smooth and all the beaten egg used, then add the sugar, walnut meats, cream, and salt and pepper to taste.
Take the celeriac roots, clean, scrub and scrape them. Cut off a slice from the top of each to make a cover, then with an apple corer remove the inside, taking care not to pierce the root, leave a shell a quarter of an inch thick. Fill each with the dressing, leaving fully half an inch at the top for it to swell. Place the cover on each, tie well the roots to prevent breaking in the cooking, stand them in a saucepan with water to reach not quite to the top of the roots, and put in all the celeriac removed from the roots, boil gently until tender, about an hour, adding boiling water from time to time as it evaporates. When they are tender take them out of the water and put them aside, keeping them hot.
Strain the water they were boiled in, form what is left from the stuffing into small cylinders, boil five minutes in the strained stock, take them out and put with the roots to keep warm.
Then make the sauce. Take the butter and flour, brown them together in a spider, add the walnuts and let them brown a little, then stir in gradually the stock the roots were boiled in and cook until it thickens.
Arrange the roots in the center of the platter, the cylinders around them and pour the sauce over all. Garnish with parsley, putting a tiny sprig of celery leaves in the top of each root.