1.Add water, 1 teaspoon soy sauce, sesame oil, cornstarch, and 1 teaspoon vegetable oil to the chicken in a medium bowl, mix well with your hands so the chicken absorbs all the marinade liquid, and set aside.
2.Prepare the sauce by mixing together broth, sugar, 1 tablespoon soy sauce, dark soy sauce, 3/4 teaspoon sesame oil, 1/8 teaspoon white pepper, and 2 teaspoons cornstarch.
3.When ready to cook, preheat your wok over medium high heat until it’s almost smoking. Add 2 tablespoons oil to the wok and sear the chicken until it’s just browned. If your wok is as hot as it should be, the chicken should not stick.
4.Turn off the heat while you transfer the chicken to a separate bowl. Leave any oil/fat in the wok. With the heat at medium-high, add 2 additional tablespoons oil to the wok.
5.Add the string beans in a single layer. Sear the string beans on one side, about 1 minute. Stir-fry the beans for 30 seconds, and then add 1/4 cup water to the wok. Cover the wok and allow the green beans to steam for 60-90 seconds (still on medium high heat).
6.Add the garlic and stir-fry for another 30 seconds. Spread the rice wine around the wok to deglaze it, stir-frying for 15 seconds. Then stir up your sauce mixture to make sure the cornstarch is well incorporated, and add the sauce to the wok. Bring it to a simmer.
7.Add the chicken back to the wok and stir-fry everything together for another 30 seconds. The cornstarch in the sauce mixture will thicken it. When the sauce is at the consistency you’d like, plate and serve immediately with rice.