Slice chicken breasts against the grain into even strips.
In a bowl, whisk together soy sauce, brown sugar, rice vinegar, sesame oil, neutral oil, grated ginger, garlic, and black pepper.
Add chicken and toss to coat. Set aside to marinate while preparing the broccoli.
Preheat oven to 425°F.
Toss broccoli florets with olive oil, salt, and pepper. Spread evenly on a foil-lined sheet pan and roast for 12–15 minutes, until lightly browned.
Push broccoli to the sides of the pan. Add marinated chicken to the center in a single layer.
Return to the oven and roast for 10–12 minutes, until chicken is nearly cooked through.
While the chicken cooks, pour the remaining marinade into a small saucepan. Simmer for 5–7 minutes, until reduced into a glossy ginger soy glaze.
Brush the glaze over the chicken. Broil for 2–3 minutes, watching closely, until caramelized.
Remove from oven, toss chicken and broccoli together, and serve over rice.
