In a small saucepan, add the eggs and enough water to cover by 1 inch; bring to a rapid boil and let cook 2 minutes. Remove and let the eggs rest in the water for 10 minutes. Let cool, then shell. In each egg, make 6–8 shallow slashes lengthwise to allow the flavors of the stew to enter.
Smack the spring onion and ginger gently with the flat side of a cleaver or a rolling pin to loosen their fibers.
In a medium saucepan, add the pork and enough water to cover; bring to boil, then let boil 5 minutes. Drain and rinse the pork with cold water. When cool enough to handle, cut into 1-inch cubes.
Heat the oil in a seasoned wok over high heat. Add the ginger, onion, star anise, and cinnamon and stir-fry briefly until aromatic (about 2 minutes). Add the pork and cook until the meat is faintly golden and some of the fat is rendering, 1–2 minutes. Splash the Shaoxing wine around the edges of the pan. Add the eggs, water or stock, light soy sauce, 2 teaspoons dark soy sauce, and the sugar. Bring to a boil, then reduce to a simmer; cover and let cook 45 minutes, stirring occasionally.
Pour into a bowl, let cool, then chill until the fat congeals (a few hours or overnight). Remove and skim away any fat that has settled on the surface. Pour the meat and liquid back into a wok, then boil, stirring constantly, to reduce the sauce by half, 10–15 minutes. Discard the ginger, spring onion, and whole spices. Stir in the remaining 2 teaspoons dark soy sauce.
Shortly before serving, bring back to a boil over high heat and reduce the sauce to about 1 inch of dark, sleek gravy. Transfer to a rimmed serving dish. Serve with rice.