Heat the oven to 350 degrees. Heat 1 tablespoon peanut oil in a large ovenproof skillet. Season about 2 pounds of pork belly, preferably with the skin on, with kosher salt and freshly ground pepper. Add the pork to the skillet, with the fattiest side or skin side down in the pan. Brown it well on all sides (about 15 minutes), and then remove belly to a plate. Pour off all but 2 tablespoons of the fat and add 1 onion, 2 carrots, and 2 celery stalks (all peeled and coarsely chopped), 1 leek (white part only, trimmed, rinsed well, and chopped), and 2 peeled garlic cloves.
Cook the vegetables, stirring occasionally, until they are tender and beginning to brown, about 20 minutes. Return the pork belly to the pan, fattiest side or skin side up, and add enough chicken stock to almost cover the meat (you will need about 3 cups of chicken stock for this recipe). Bring the stock to a simmer, and then move the pan into the oven. Cook uncovered for about two hours, adding more stock if necessary, until the pork is tender enough to cut with a fork (test it!). This will take some time. The top should be nicely browned. The meat will have shrunk as some of the fat is rendered.
Remove the pork from the pan. Strain the liquid, discarding the vegetables. Use a gravy separator to separate as much of the liquid from the fat as possible. Serve a piece of the pork with some of the liquid, preferably with polenta or mashed potatoes to help soak up the gravy!