Rinse the chicken and trim off any excess fat. This recipe calls for whole chicken leg quarters, but you can cut them into drumsticks and thighs for easier handling in the wok if desired.
Heat 2 tablespoons of oil in your wok or a large frying pan over medium high heat, spreading the oil around to coat. Place the chicken skin-side-down in the pan carefully, and sear for about 3 minutes, or until golden brown.
Next, flip the chicken and add the smashed ginger slices to the bottom of the pan. Let both sides of the ginger slices cook and caramelize in the oil for 1 to 2 minutes.
Next, add the garlic slices and white portions of the scallions. Let fry in the oil for a minute. Use a metal spatula to ensure the chicken is not stuck to the wok, but be gentle so as to not break up the chicken skin.
Add the Shaoxing wine to deglaze the pan, and let cook for another 1 to 2 minutes. Add the chicken stock, soy sauce, oyster sauce, white pepper, and sesame oil. Stir until well combined and bring the liquid to a boil. Reduce the heat to a slow simmer. Cover and let cook for 15 minutes.
Use tongs or chopsticks to turn the chicken quarters and let cook for another 15 minutes. There should be quite a bit of sauce in the pan, but if things are looking dry, add a bit more chicken stock.
Next, uncover the chicken and add the green portions of the scallions. Cook uncovered to reduce the liquid until it just begins to coat a spoon. Use a meat thermometer to check to make sure the internal temperature of the chicken is 165 degrees F. Alternatively, you can just poke the thickest part of the chicken leg quarter with a fork--the juice should run clear. At this point, you can be the judge of how thick or thin you want your sauce to be, but the chicken should be done. Turn the heat up to reduce the sauce if you like yours on the thicker side.
Serve the chicken, all of that luscious gravy, and the cooked down garlic, ginger, and scallions over a bed of white rice with your favorite veggies. Stir-fried bok choy or garlicky broccoli are great choices.