Marinate the Chicken : In a medium bowl, combine the chicken pieces with ½ tablespoon minced garlic, ½ tablespoon minced ginger, soy sauce, ½ tablespoon coarse salt, and Shaoxing wine. Toss to coat and let marinate for 15–20 minutes while preparing other ingredients.
Prepare the Sauce : In a small bowl, whisk together the brown sugar, cornstarch, and ⅓ cup water. Set aside.
Cook the Chicken : Heat 2 tablespoons vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken in a single layer and cook for 5–7 minutes, stirring occasionally, until lightly browned and cooked through. Remove the chicken from the skillet and set aside.
Stir-Fry the Vegetables : Add 2 tablespoons vegetable oil to the skillet and heat over medium-high heat. Add the broccoli florets, sweet onion, and 1 teaspoon minced ginger. Stir-fry for 3–4 minutes, or until the broccoli begins to soften. Add 1 teaspoon chili garlic sauce, ¼ cup water, and a pinch of salt. Cover and steam for 2–3 minutes, or until the broccoli is tender but still crisp.
Combine Everything : Add the cooked chicken back into the skillet with the vegetables. Pour in the prepared sauce and toss everything together. Cook for 2–3 minutes, allowing the sauce to thicken and coat the chicken and vegetables.
Add Finishing Touches : Drizzle 2 tablespoons sesame oil over the stir-fry and toss to combine. Garnish with diced scallions.
Serve : Serve the Chicken and Broccoli Stir-Fry over freshly cooked white rice. Enjoy!