Dredge the pieces of meat in seasoned flour and brown them well in fat in a large frying pan over a hot flame. At the same time cook the onions and carrots in enough salted water to cover. As the pieces of meat are done, put them into a 3-quart deep pie dish alternately with the onions and carrots. Slice the mushrooms into the frying pan with more butter, cook briefly, and add to the casserole. To the juices in the pan add the remaining flour and garlic. Gradually pour in the water in which the vegetables were cooked, plus the beef stock and red wine, stirring to make a smooth sauce.
Season the sauce with herbs as available, fresh or dried parsley or chervil, marjoram or thyme, chives or green onions. Taste the sauce. If you wish, add more salt or herbs, or a dash of Kitchen Bouquet to taste. Pour it over the meat and vegetables. Make a pie crust. Fold it, slash it in several places to let steam escape, put it over the pie and flute the edges. Glaze the crust if you wish by brushing egg yolk over the surface and ornament it with pastry cut-outs. Put the pie in a 350 degrees F oven 50 or 60 minutes before you are ready to eat it.