Preheat the oven to full whack (about 250°C fan-forced).
Place the beef in a casserole dish or a deep roasting tin. Add the garlic, tomato paste, rosemary, salt, pepper and anchovy fillets and use your hands to rub the ingredients into the beef. Pour over the red wine, beef stock and balsamic vinegar and cover with baking paper (this reduces evaporation). Pop the lid on or tightly seal with foil. Sealing the dish traps in the steam, which results in incredibly tender meat.
Place the dish or tin in the oven and set the timer for 20 minutes. After 20 minutes, reduce the oven temperature to 160°C (150 fan-forced) and cook the beef for 3 ½–4 hours, or until the meat is falling apart. Skim off the layer of fat that might have formed on the surface, then, using two forks, shred the beef and mix everything together. Discard any chunks of fat.
Bring a large saucepan of water to a lively boil and season as salty as the sea. Add the pasta and cook until al dente.
Scoop out 250 ml (1 cup) of the pasta cooking water, then drain the pasta and transfer to a large serving bowl. Add large scoops of braised beef and give everything a good toss around, adding 125 ml (½ cup) of the cooking water if you need to loosen things up. Stir again and add a little more cooking water if needed. Stir through lots of Parmigiano Reggiano and serve with a little extra sprinkled on top.