Saute bacon. Remove pan from heat and drain grease. Add chipped beef, butter and mushrooms to pan with bacon. Sprinkle flour and pepper over mixture. Gradually stir in milk. Cook until sauce is thickened and smooth.
Stir constantly. Set aside. Combine eggs with salt and milk. Scramble in butter in a large skillet. In a 9x13 casserole dish, alternate layers of 1/2 eggs, 1/2 sauce, 1/2 eggs, 1/2 sauce. Cover with foil or casserole lid and bake at 275 for 1 hour.