How to Make It
In a saucepan, bring the water to a boil with the sugar and salt. Add the vinegar, ginger and peppers. Transfer to a heatproof bowl; let cool. Cover and refrigerate overnight or up to 1 week.
Preheat the oven to 300°. In a medium enameled cast-iron casserole, heat 1 tablespoon of the oil. Season the pork with salt and black pepper and add to the casserole. Cook over moderately high heat, turning a few times, until richly browned, 12 minutes; transfer to a plate.
Pour off the fat in the casserole. Return the pork to the casserole. Add the stock, mirin, soy sauce, garlic, onion, ginger and crushed red pepper. Bring to a boil. Cover and braise in the oven for 3 hours, turning the pork once, until the meat is very tender. Transfer the pork to a work surface; slice into 4 equal pieces. Strain the braising liquid. Return the meat to the casserole, top with the liquid, cover and simmer until warm.
In a nonstick skillet, heat the remaining 1 tablespoon of oil. Crack in the eggs and fry them over easy over moderate heat. Spoon rice into bowls and top with the pork. Ladle the braising liquid over the meat and top with the eggs. Garnish with the peppers, scallions and a dab of mustard and serve.