Heat oil in a large skillet over medium-high heat until shimmering.
Toss chicken with 1 tablespoon cornstarch until evenly coated.
Add chicken to skillet in a single layer and cook until crisp and cooked through, about 6 minutes.
Add onion and cook until translucent, about 1 minute. Add ginger and garlic and cook until fragrant.
Transfer chicken mixture to a plate and set aside.
Add broccoli to the skillet and cook until bright green and tender-crisp, 2 to 3 minutes.
Whisk water, soy sauce, oyster sauce, brown sugar, red pepper flakes, black pepper, and remaining cornstarch.
Return chicken to skillet, add sauce, and cook until thickened and glossy, about 2 minutes.
Serve immediately over rice, if desired.