Step 1Heat the oven to 425 degrees. In a large saucepan heated over high heat, bring the chicken broth to a boil, then remove from heat. Set aside.
Step 2Place a large saute pan over medium heat, then add the olive oil. Place the carrot, onion, celery and garlic in the pan. Cook, stirring, until they are golden brown, 10 to 15 minutes, and add the tomato paste, rosemary and sage sprigs. Cook, stirring until the vegetables are coated and the herbs are fragrant, 2 to 3 minutes.
Step 3Transfer the vegetable mixture to a casserole dish. Place the pork belly pieces on top of the vegetables. Pour in the chicken stock. Cover the dish with aluminum foil and slide it into the oven. Braise the pork belly until you can squeeze tongs easily into the meat, with little resistance, 1 1/2 to 2 hours. Remove from the oven.
Step 4Make the sauce: Strain the broth and let it sit for a few minutes, allowing the fat to rise to the surface. Skim the fat off the stock and pour the stock into a large saucepan. Bring to a simmer and cook until the sauce is reduced enough to thickly coat the back of a spoon, about 15 minutes. Add the butter, vinegar and sage. Taste the sauce and season it with salt and pepper accordingly. Let the sauce sit on the back of the stove or in a warm place while you finish the pork belly.
Step 5Place 3 slices of bacon per piece of pork belly on a plate, overlapping them like ribbons. Season each piece of pork belly with a pinch each of salt and pepper on both sides. Place each pork belly piece, skin side down, in the middle of the bacon. Fold the bottom part of the bacon ribbon up over the belly, and then bring the top down.
Step 6Pour the canola oil into a clean, oven-safe saute pan or baking dish. Put the bacon-wrapped pork belly, seam side down, into the pan. Slide the pan into the oven. Cook, turning halfway through, until the bacon is crisp, 10 to 15 minutes. Take care not to burn yourself, because the bacon fat will continue rendering, spitting hot fat. Carefully remove from the oven. To serve, spoon a bit of sauce over each piece of pork belly.