Make the sauce: In a small bowl whisk together soy sauce, chicken broth, minced garlic, honey, hoisin sauce, oyster sauce, rice vinegar, cornstarch, and grated ginger until smooth; set aside.
Heat 1 tablespoon oil in a large skillet over medium-high heat.
Add the diced chicken to the hot skillet, season with the black pepper, and sauté 5–7 minutes, stirring frequently, until cooked through; remove chicken with a slotted spoon and keep warm, leaving pan juices behind.
Add the remaining 1 tablespoon oil to the skillet, then add the sliced onion, mushrooms, and broccoli; sauté 4–5 minutes, stirring often, until vegetables are becoming tender-crisp.
Pour the prepared sauce over the vegetables, bring to a simmer, and cook 3–4 minutes, stirring, until the sauce begins to thicken and coats the vegetables.
Return the cooked chicken to the skillet, toss to coat and rewarm about 1 minute; taste and adjust seasoning with salt if desired.
Serve immediately and optionally garnish with sesame seeds.
