Place the dried shiitake mushrooms in a heatproof bowl and cover with 1/2 cup (120 ml) hot water. Soak until softened, then remove the mushrooms and finely chop them. Reserve the soaking liquid, leaving behind any gritty sediment in the bottom of the bowl.

Set a Dutch oven or heavy-bottomed pot over medium heat. Add the pork belly and cook, stirring occasionally, until some fat has rendered and the pork is lightly browned, about 8 to 10 minutes. Carefully spoon off excess fat, leaving about 1 tablespoon in the pot.

Add the shallots, garlic, and chopped mushrooms. Cook, stirring often, until fragrant and softened, about 3 minutes.

Stir in the regular soy sauce, dark soy sauce, Shaoxing wine, brown sugar, reserved mushroom soaking liquid, remaining 1 1/2 cups (360 ml) water, star anise, five-spice powder, and white pepper. Scrape up any browned bits from the bottom of the pot.

Bring the liquid to a gentle simmer. Reduce the heat to low, cover partially, and simmer for 40 minutes, stirring once or twice so the pork does not stick.

If using hard-boiled eggs, nestle them into the sauce. Continue simmering, uncovered or partly covered, until the pork is tender and the sauce has thickened enough to coat a spoon, about 15 to 20 minutes. Remove and discard the star anise. Taste and add a small splash of water if the sauce is too salty or thick.

Divide the hot rice among six bowls. Spoon the braised pork and sauce over the rice, add a halved egg and greens if using, and finish with sliced scallions.