For the pork belly, rub the meat all over with the salt and sugar, and put it in a bowl, covered, overnight. The next day, preheat the oven to 450℉ and then roast the pork for 30 minutes. Decrease the oven temperature to 275, and let the pork ride out for 1 hour more. Once finished, let cool to room temperature and refrigerate.
For the tare, roast the chicken at 450ºF until dark golden brown. In a wide saucepan, combine the soy sauce, rice vinegar, and mirin, bring to a simmer, and then add the chicken back and bacon. Reduce the heat to the barest simmer, cooking for an hour. The goal here is not to reduce, but to imbue the liquid with chickeny, smoky, cured pork flavors.
Finally, make the broth. Bring 1.25 gallons of water and the kombu to a boil in a very large pot. Once it boils, turn off the heat, and let the kombu steep for 20 minutes. Remove the kombu, add the chicken parts, and bring back to a boil. Then add the shiitake powder and ginger. Reduce to a simmer and simmer for 5 hours, then let cool and strain, first to remove the solids and then through a fine mesh sieve.
Just before serving, make the eggs. Bring a pot of water to a boil, carefully add the eggs, and maintain at a high simmer for 6 minutes and 10 seconds. Meanwhile, prepare an ice bath. Quickly remove the eggs to the ice, and peel, using the water to help get off the shell. Be careful, because the whites will still be delicate and the yolks runny.
To assemble, bring the stock to a boil and cook the noodles according to package directions in a pot of boiling water. Slice the pork belly into thin slices, and crisp up in a pan with a splash of oil or in the oven at 350℉. To 5 wide soup bowls, add about 1 tablespoon of the tare, then a large ladleful of broth. Add the noodles, pork belly, and nestle in the egg. Garnish as desired and serve, piping hot.