* Ground beef should only be ground once and be the leanest you can get. ~- In a frypan saute onions and mushrooms in vegetable oil until soft. Add ground beef; saute mixture 3 to 4 minutes. Stir in broth; bring to a simmer. Add 1/2 t nutmeg, worcestershire sauce, 1/2 t salt, and 1/4 t pepper. Peel the potatoes and boil them in salted water until tender, about 30 minutes. Drain and put through a food mill or grinder. Beat in 2 T butter, 1/2 t salt, 1/4 t pepper. Adjust seasonings to taste. Beat in eggs and remaining nutmeg. Peel, core, and slice apples. Layer mixtures in a 1 1/2-quart buttered baking dish. Spread 1/3 of potatoes on bottom of dish. Top with 1/2 of the meat mixture and 1/2 of the apples. Continue with layers, ending with a layer of potatoes. Sprinkle the top with bread crumbs, and dot with remaining butter. Bake at 375 degrees F. for 45 minutes and then at 400°F for 10 minutes more.