Preheat oven to 350°. 

Heat a deep sided roasting tray on the stove top and add some olive oil on the tray.  Season the short ribs with salt and pepper and fry them for 10-15 minutes until they are brown on all sides.  

Add the halved garlic head, cut side down, pushing it to the bottom of the pan.  Add the tomato puree and heat for a minute or two to cook it out.   Pour the wine to deglaze the pan, scraping up the bits at the bottom.  Bring to a boil and cook for 10-15 minutes until the liquid is reduced by half.   Add the stock to nearly cover the ribs (you'll need less stock if your roasting tray isn't very large).   Bring to a boil again, basting the ribs with the juices.  

Cover the roasting tray with foil and cook in the oven for 3-4 hour, basting now and then until the meat is tender and falling away from the bone.  

About 10 minutes before the short ribs are ready to come out, fry the pancetta for 2-3 minutes until crisp and golden.  Add the mushrooms and cook for 4-5 minutes until tender.  Drain off any excess fat.  

When the ribs are ready, remove from the oven and transfer to a serving dish.  Squeeze the garlic cloves out of their skins and pass through a sieve.  Spoon off any excess fat from the beef cooking liquid, then strain it through the sieve and mix with the garlic.   If the sauce is too thin, reduce the cooking liquid by heating it for 10-15 minutes more after straining.  

Serve the short ribs topped with the pancetta and mushrooms and the sauce poured around.  Garnish with chopped flat leaf parsley.