In an 10 to 12 quart stock pot or soup kettle combine beef with short ribs and cover with stock or water by 4 inches. Bring to a boil over moderate heat; as the stock begins to boil, carefully skim all foam and scum from surface and discard. Reduce heat to low, skim again, then add onions, carrots, tomatoes and bouquet garni. Skim again; cover the pot, leaving the lid ajar and simmer as slowly as possible, skimming on occasion. Cook for 2 to hours or until meat is almost tender. Remove meats. Strain the liquid through a sieve lined with dampened double layer of cheesecloth. Discard seasoning vegetables and bouquet garni; remove surface fat. (If you do this on one day, before you finish the dish, store meat and liquid separately.)
Transfer stock to a clean pot. Return the meat to the liquid along with the carrots and turnips. Bring the liquid to a boil, season with salt and pepper and simmer for 30 minutes or until carrots, turnips and meats are tender. Meanwhile boil the potatoes separately (when done, leave in water off heat) and steam cabbage wedges separately for 8 minutes or until just tender.
To serve, degrease the liquid and season with salt and pepper. Remove meat from liquid, discard strings and carve into 1/4-inch slices, remove short rib bones and cut into chunks. Transfer slices of meat, a portion of potatoes, cabbage, carrots, turnips into a deep soup plate. Ladle liquid over the top and garnish with parsley; serve as main course soup.
Or, serve soup liquid first, garnished with parsley and serve meat, vegetables, potatoes and carrots as a second course, accompanied by 1 or more accompaniments and a good French bread.