Begin by preparing the pork belly. Preheat the oven to 400 degrees. Remove the skin from the pork and dry it off with paper towels.
Sprinkle it all over with the sugar, salt, and pepper. Put it in a ceramic casserole dish and bake for thirty minutes. Turn the heat down to 275 degrees and roast it for 40 more minutes. Remove it from the oven and let it cool off a little and then refrigerate it for at least a hour.
Meanwhile, boil the ramen noodles according to the package directions and then drain them.
Also, in a skillet, on medium heat, cook the Swiss chard in a tablespoon of vegetable oil until it's wilted and softened.
Also, prepare the eggs: Place the eggs in a three quart saucepan and cover with water. Bring the pot to a boil, and then cover the pot and remove it from the heat. Let the eggs sit in the water for six minutes. Then, drain the eggs and peel them. Cut the eggs in half.
In a Dutch oven, heat a tablespoon of vegetable oil and then add the yuzu miso and ginger. Cook for one minute and then add the chicken stock and carrots.
Bring it to a simmer and keep it warm until you're ready to plate the soup.
In a cast iron skillet, heat another tablespoon of oil on high heat. Slice the pork into thin slices and cook it on both sides, until it start to get crispy.
Divide the broth between 4 bowls. Add the noodles, pork belly, Swiss chard, eggs, mushrooms, carrots, and peppers. Then, sprinkle on the scallions, and sesame oil.