Cut 1 pound boneless, skinless chicken breast into bite-sized pieces, then toss in a bowl with 1 tablespoon soy sauce and 1 tablespoon cornstarch; set aside to marinate.
Prepare vegetables: cut 2 cups broccoli florets, slice 1 cup carrots into thin rounds or matchsticks, slice 1 medium red bell pepper, mince 2 cloves garlic, and grate 1 tablespoon fresh ginger.
In a small bowl, whisk together 1/4 cup Shaoxing rice wine, 1/4 cup soy sauce, 1 tablespoon sesame oil, 1 tablespoon cornstarch, and 1/2 cup water until smooth.
Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat until shimmering. Add the marinated chicken in a single layer and cook 4–5 minutes, stirring occasionally, until lightly browned and cooked through (165°F). Remove chicken and set aside.
Add the remaining 1 tablespoon vegetable oil to the skillet. Stir-fry the garlic and ginger 30 seconds until fragrant.
Add the broccoli, carrots, and red bell pepper. Stir-fry 5–7 minutes until vegetables are crisp-tender.
Give the rice wine sauce a quick whisk, then pour into the skillet. Bring to a simmer, stirring constantly, until sauce thickens and coats the back of a spoon.
Return the cooked chicken to the skillet and toss with the vegetables and sauce until heated through and well coated.
Serve immediately over steamed white rice.