Trim excess fat from the chicken thighs then cut into 1-inch cubes. Transfer chicken to a bowl, sprinkle with salt, and mix well.
In a mixing cup, combine sesame oil, light soy sauce, dark soy sauce, shaoxing wine, sugar, chicken broth, and cornstarch. Mix well and set aside.
Heat 1 tablespoon of vegetable oil in a wok over medium-high heat. Add chicken and sauté until golden brown on all sides, about 4-5 minutes. Add garlic and ginger and stir-fry until fragrant, about 1-2 minutes.
Pour in the sauce and stir to combine. Lower the heat, cover, and let simmer for 10 minutes, stirring occasionally. If the sauce reduces too quickly, add a splash of water.
Toss in the Thai basil, stirring until the basil is just wilted, about 1 min, then turn off the heat. Serve hot with steamed white rice.