Generously season beef short ribs with salt and pepper.
Preheat heavy bottom stock pot or Dutch oven over medium high heat with a glug of olive oil. Add short ribs and brown well on all sides; about 10-15 minutes.
Remove short ribs from pot and set aside. Lower heat to medium.
Add the halved garlic heat, cut side down to the hot pot. Push it to the bottom to sear. Add the tomato paste and heat for a minute or two. Pour in the wine to deglaze the pan, scraping up the bits at the bottom.
Bring to a coil and cook for 10-15 minutes or until liquid is reduced by half.
Place browned ribs in bottom of a large crockpot. Pour over cooked wine sauce. Top with beef stock to completely cover short ribs.
Cook on LOW heat for 6-8 hours.
About 10 minutes before serving, fry the pancetta for 2-3 minutes or until crisp and golden. Add the mushrooms and cook another 4-5 minutes. Drain off excess grease.
Transfer short ribs to a serving dish. Squeeze the garlic heads into a wire sieve and press through into sauce in crockpot. Mix well. (If sauce seems too thin, turn your slow-cooker to HIGH. Mix a bit of the liquid with cornstarch to make a slurry. Pour back into the slow cooker and allow to cook until thickened to your liking.)
Serve the short ribs topped with the hot pancetta and mushrooms. Pour the sauce over. Garnish with chopped fresh parsley, as desired.
