Score both sides of the pork belly with the tip of a sharp knife in a ½-inch crosshatch pattern and rub with the vanilla paste. Combine the salt, brown sugar, five-spice powder, and blackpepper in a small bowl and rub both sides of the belly with the mixture. Place the meat in a large, wide not-reactive container. Cover with plastic and refrigerate overnight.
Preheat the oven to 325˚F.
Heat the oil in a large, wide casserole or sauceplan over medium heat and add the onions, carrots, and celery. Cook the mixture, stirring occasionally, until lightly browned, 8 to 10 minutes. Add the lemongrass, ginger, and kaffir lime leaves and continue to cook for 2 or more minutes, or until aromatic.
Add the black vinegar and bring to a boil over high heat, stirring and scraping the bottom of the pan to deglaze. Cook until the liquid has evaporated, 5 to 8 minutes.
Add the plum wine, red wine, and sake and bring to a boil. Reduce by half, 20 to 30 minutes. Add the veal stock and chicken stock and bring to a boil.
Grill the pork belly on both sides over medium heat until nicely browned, about 10 minutes per side. Place in the pot with the broth and vetables. Cover with aluminum foil, and place in the oven. Cook until the meat is fork tender, 1 ½ to 2 hours.
Lift the pork belly out of its cooking broth and transfer it to a cutting board (keep the broth hot until ready to serve). Slice the belly up 6- or 7-inches long by ¼-inch wide strips and place 4 in each of 8 bowls. Taste the broth; if it’s too salty or concentrated for use as a dipping sauce, add water to thin it a little. Pour ¼ cup of hot broth into each bowl and serve immediately.