Cut pork belly into 1 inch cubes. Put them into a pot and fill with cold water. Boil over high heat. Once boiled, skim off the froth if there is any.
Add 2 green onions and 3 slices of ginger into the pot. Put the lid on, simmer the pork belly over low heat for 30 minutes. (Most recipes do not have this step. This is the most special and important part from my grandpa's secret recipe! With this simmering step, the pork belly will be less oily and much tenderer!)
Drain the pork belly. Dry them up with kitchen towels.
Layer the pork belly cubes in a frying pan, pan fry over medium heat until each side turns golden brown and a little crispy. (Do not add cooking oil at this step. Pork belly will release oil.)
Transfer the pan fried pork belly cubes to a dutch oven pot. (There should be a layer of pork oil (lard) in the frying pan. You can pour the lard into a clean jar, and save it for other dishes. Lard is perfect for cooking Chinese style noodles.)
Add 2 green onions, 3 slices of ginger, ¼ cup brown sugar, ¼ cup cooking wine (Shaoxing wine), ¼ cup light soy sauce, and 1 tablespoon dark soy sauce to the dutch oven pot. Add hot water until barely cover the pork belly cubes.
Cook over medium high heat until boiled. Put the lid on. Turn to medium low heat to simmer for 1 hour.
Remove the lid. Add peeled quail eggs to the pot. Stir to cover the eggs evenly with the sauce.
Leave the pot uncovered, use medium heat to thicken the sauce for 10-15 minutes, until all the pork belly cubes and eggs are coated in glossy sauce, and there is barely no liquid left in bottom of the pot.
Serve with steamed rice and vegetables of your choice.