Brine the pork belly: Bring 7 cups water to a boil in a large saucepan. Add the salt and sugar and stir to dissolve. Let cool, then stir in the bay leaves, allspice, cloves, and peppercorns.
Pour the brine into a large bowl and put the pork belly in it. Use a heavy plate as a weight to keep the meat submerged. Refrigerate for 3 days, turning the pork belly once or twice.
The day you plan to serve, cook the pork belly: Preheat the oven to 350°F. Drain the pork belly and pick off any whole spices clinging to the meat. Pat the belly dry with paper towels. Spread the onions, carrots, garlic, and fennel in a roasting pan. Set the meat on top of the vegetables, pour in the wine, and snugly cover with a sheet of parchment paper or foil. Braise in the oven, covered, for 2 hours.
Uncover the pork and roast for 15 minutes. Turn the pork belly over and roast for 15 minutes longer, until the meat is fork tender and beautifully brown on both sides, about 30 minutes total. Remove the pork and let cool; wrap tightly, and refrigerate until well chilled and firm, at least 1 hour so it firms up. (Save all the fat in the roasting pan for cooking stews, soups, and confits.) Neatly cut off six 4-ounce portions from the chilled pork belly; wrap in paper towels and refrigerate. Freeze the rest for future use.
Make the Fava Bean Ragout through Step 1 as directed at right.
About 10 minutes before serving, preheat a stovetop grill pan over moderate heat. Set the pieces of pork belly in the hot pan. Weigh down with a bacon press or heavy skillet and grill until nicely browned, about 3 minutes. Turn over and brown the second side, 2 to 3 minutes longer.
Meanwhile, finish the Fava Bean Ragout. Arrange the ragout in a serving dish. Place the browned and crisp pork belly (petit salé) on top, garnish with the fresh herbs and serve at once.
If you purchase pork belly with the skin on, remove the skin and cut it into 3 by 8–inch pieces. Use them to make Confit of Pork Rinds (page 17); you'll be surprised how often this comes in handy. It makes an excellent addition to soups and lentil and bean dishes.
In a medium covered skillet, cook the shallots and pancetta in the duck or pork fat over moderately low heat for 5 minutes. Uncover and continue cooking until the pancetta is light brown around the edges. Add the artichoke slices, fennel slices, and sugar and cook for a few more minutes, stirring. Raise the heat to high, add ¼ cup of water, and remove from the heat. (The recipe can be prepared to this point up to 8 hours in advance. Cover and refrigerate.)
Add the stock and fava beans to the skillet. Bring to a boil, cover tightly, reduce the heat to moderate, and cook until the favas are completely tender, 3 to 5 minutes. Adjust the seasoning with salt and pepper.