In a small bowl, whisk together the soy sauce, oyster sauce, honey, sesame oil, cornstarch, chicken broth, and black pepper until smooth.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the chicken and cook for 5–6 minutes, stirring occasionally, until browned and fully cooked. Transfer to a plate.
Add the remaining tablespoon of oil to the skillet.
Sauté the onion for 2 minutes, then add the garlic and ginger and cook for 30 seconds until fragrant.
Add the zucchini and bell pepper and cook for 3–4 minutes, stirring frequently, until the vegetables are crisp-tender.
Return the cooked chicken to the skillet.
Pour the prepared sauce over the chicken and vegetables. Stir continuously for 2–3 minutes, until the sauce thickens and evenly coats everything.
Garnish with sliced green onions and sesame seeds, if desired.
Serve immediately over steamed rice, noodles, or cauliflower rice.