Velvet the chicken: In a medium bowl, toss chicken thighs with 1 tablespoon soy sauce, Shaoxing wine, 1 tablespoon cornstarch, and 1 teaspoon neutral oil. Let sit for 15 minutes.
Make the sauce: Whisk together chicken broth, oyster sauce, honey, remaining 1 tablespoon soy sauce, and 1 teaspoon cornstarch in a small bowl. Set aside.
Stir-fry the chicken: Heat a large wok over high heat until nearly smoking. Add 2 tablespoons oil and swirl to coat. Add chicken in a single layer. Cook undisturbed for 90 seconds, then stir-fry for 2 minutes until mostly cooked. Remove to a plate.
Cook the vegetables: Add remaining 1 tablespoon oil to the wok. Stir-fry bell pepper strips for 2 minutes until crisp-tender. Push to the side and add minced garlic and grated ginger to the center. Cook for 30 seconds until fragrant, then mix together.
Combine and finish: Return chicken to the wok. Give the sauce a quick stir and pour over everything. Toss continuously for 1 to 2 minutes until sauce thickens and coats everything. Finish with toasted sesame oil. Garnish with green onions and sesame seeds. Serve immediately over jasmine rice.