1. Preheat the oven to 375F.
2. In a medium bowl, add the chicken, egg white, cornstarch, salt, pepper, soy sauce, and sesame oil. Mix to combine and marinate for at least 15 mins at room temp (or up to 4 hours in the fridge).
3. Drizzle 2 Tbsp sesame oil onto a sheet pan and add the broccoli, tossing to coat. Arrange the chicken around the broccoli, spreading it into an even layer so it touches the pan. Sprinkle with the chopped ginger and bake for 15 mins.
4. In a medium glass measuring cup or heatproof bowl, whisk together the chicken stock, garlic, cornstarch, soy sauce, oyster sauce, sesame oil, white vinegar, sugar, and pepper until combined. Microwave for 2-3 mins, pausing once or twice to whisk, until the sauce is bubbling and thickened (or cook in a small saucepan over medium heat, whisking constantly, until bubbling and thickened, 3-5 mins).
5. Spoon the sauce onto the chicken and broccoli and toss to coat. Sprinkle with the scallions and sesame seeds and return to the oven for 5 more mins.
6. Serve over rice and enjoy!