Making the Pestata and Starting the Braise: Using the food processor with the metal blade, mince the bacon and garlic cloves together into a fine pestata (paste). Since you have the machine out, use it to chop the carrot, celery and onion if you want (you dont need to wash the bowl). Process each vegetable separately: cut the carrot and celery stalk into chunks before chopping; pulse each to small bits. Chunk up the onions into 1-inch pieces, put them into the food processor bowl in batches, and pulse them to 1/4-inch bits, not too fine. Put the onions into a big bowl-you will have 4 to 5 quarts of chopped onion when you are done. (Of course, you may shred and chop the vegetables by hand, or even mince the bacon-garlic paste with a heavy cleaver as I did growing up. It takes longer but is quite satisfying.) Rinse and dry the pork, then sprinkle about 1/2 teaspoon salt lightly on all surfaces, patting it on. Pour the oil into the braising pan and set it over medium heat. Before it gets hot, lay the pork in and brown it-lightly-turning it after a minute or so on each side. While the meat is browning, scrape the pestata into the pan bottom; spread it out and let the bacon begin to render. Drop in peperoncino now, if you want some heat in the salsa; toast it in the pan bottom. After 3 minutes or so of browning the pork, drop the tomato paste into the fat; stir and caramelize a minute. Dump the shredded carrot and celery into the pan bottom; stir for a minute just to get them cooking. (Keep turning the meat so it browns evenly and slowly.) Now scrape the chopped onions into the pan, all around the meat. Sprinkle the remaining coarse salt over the onions; raise the heat a bit, stirring the onions up from the bottom and mixing them with the oil, pestata and tomato. Cook on medium high heat, stirring, for about 5 minutes until the onions are all hot and starting to sweat. Cover and turn the heat to medium-low. Braising the pork: The pork is now going to cook for about 3 hours. Leave it alone for the first 45 minutes, then uncover, turn the meat and stir the onions. They should be wilting and releasing liquid; if there is any sign of burning, lower the heat. Cover and cook for another 45 minutes, turn the meat and stir the onions. They should be quite reduced in volume, in a thick simmering sauce. Stir in 2 cups of hot broth, bringing the liquid higher around the pork. Cook covered for another 45 minutes, then stir. If the sauce level has dropped a lot and is beginning to stick, stir in another cup or 2 of broth. Taste and add more salt, if necessary. Cover and cook another 1/2 hour to 45 minutes. Check the consistency of the onions-they should be melting into the sauce and the meat should be soft when pierced with a fork. If satisfactory, remove from the heat; otherwise cook longer, adding more broth, or if the sauce seems thin, uncover and cook to reduce it.