To prepare the ragu, cut beef away from the rib bone and into large chunks, reserve the ribs. Dust meat and ribs with some salt, pepper and flour and brown in some hot butter in a large stock pot. Add diced carrot and celery stalks, mix and cover with stock, water and wine. Bring to a boil then lower heat to a very gentle simmer.
Scoop off any brown foam that may form with a ladle and discard. Cook uncovered for about 1 hour.
Preheat oven to 160C (140C fan forced, 325F, gas mark 3).
Transfer the meat, stock and vegetables into an oven-proof roasting tin, cover tightly with aluminium foil and cook in the oven for a further 2 hours, or until the meat is falling apart to the touch, checking after an hour that the stock hasn’t all evaporated. Add extra water if needed. Turn the oven off and allow the meat to rest, covered for about 20 minutes in the warm oven.
Discard celery stalks and shred the meat using a fork.
To make the sauce, heat butter in a saucepan big enough to hold the meat as well. Add pepper and mushrooms and stir until lightly cooked. Add meat and pasta sauce. Warm through as you prepare pasta according to its cooking instructions.
Drain pasta and serve with a generous dollop of ragu on top.