Heat neutral oil in a large skillet or wok over medium-high heat.
Add chicken pieces and cook until browned and cooked through, about 6-8 minutes. Remove and set aside.
Steam broccoli florets until tender-crisp, about 4-5 minutes.
In a small bowl, whisk together soy sauce, chicken broth, cornstarch, sesame oil, minced garlic, and grated ginger until smooth.
Return chicken to the skillet and add steamed broccoli.
Pour sauce over chicken and broccoli, stirring constantly until sauce thickens, about 2-3 minutes.
Serve immediately over rice and garnish with sesame seeds.