Whisk soy sauce, oyster sauce, rice vinegar, brown sugar, broth, 1.5 tsp cornstarch, and 1 tsp black pepper until smooth.
Pat chicken dry. Toss with salt, 3 tbsp cornstarch, and 0.5 tsp black pepper to coat evenly.
Heat 2 tbsp oil in a large skillet over medium-high until shimmering.
Sear chicken in a single layer, working in batches if needed, until lightly browned and just cooked, 4–5 minutes total. Transfer to a plate.
Add remaining 0.5 tbsp oil. Stir-fry onion and bell pepper until crisp-tender, 2–3 minutes.
Stir in garlic and ginger. Cook until fragrant, about 30 seconds.
Return chicken and any juices to the pan and toss with the vegetables.
Pour in the sauce. Cook, stirring, until thick and glossy, 2–3 minutes.
Finish with sesame oil and the remaining 0.75 tsp black pepper. Toss and sprinkle with scallions.