Adjust oven setting to broil.
Using a sharp knife, score the fat side of the pork belly, diagonally, and season with salt and pepper on all sides. Place apples, onion, carrots, and celery in the bottom of a large roasting pan. Place the pork belly, scored side up, on top of the vegetables. Broil until golden brown, about 15 minutes. Turn the pork flesh side up and continue broiling for 10 more minutes.
Reduce the oven temperature to 300 degrees F.
Turn the pork back to the scored side up and add the chicken stock, 2 cups of the apple cider, light brown sugar, thyme, cloves, and allspice to the roasting pan. Cover the pan with foil and bake for 2 hours. After 2 hours, remove the apples, fold back the foil to create a vent and continue to bake for another 2 hours or until the meat is very tender. Keep the apples for garnish.
While the pork is braising, prepare the cider glaze: Combine the juice and 3/4 cup of sugar in a medium saucepan and bring mixture to a boil. Reduce heat to a gentle boil and cook until the glaze is thick and syrupy, about 30 to 40 minutes. (The finished glaze will form dime-sized bubbles while simmering and will be thick enough to coat the back of a spoon.)
Remove the pan from the oven and let the pork cool slightly in the braising liquid. Adjust oven setting to broil. Remove the pieces of pork belly from the braising liquid and pat dry. Using a pastry brush, baste the pork belly on all sides with the glaze. Place on a baking sheet lined with aluminum foil and broil for 4 to 5 minutes, or until crispy around the edges and golden brown.
Drizzle pork belly lightly with some of the remaining glaze.