1. Mix broth, soy sauce, garlic, honey, cornstarch, ginger, and sesame oil in a small bowl until the cornstarch dissolves.
2. Heat neutral oil in a large skillet or wok over high heat. Cook chicken without moving until it releases easily from the pan, about 1 to 2 minutes. Stir and continue cooking until golden brown on all sides and fully cooked, about 5 minutes more. Remove from heat and set aside.
3. Toss broccoli in the broth mixture in the same skillet over medium-low heat. Cover the skillet and steam the broccoli until crisp-tender, about 2 to 3 minutes.
4. Return the chicken and any accumulated juices to the skillet. Cook, stirring, until the sauce thickens and the chicken and broccoli are well coated, about 1 to 2 minutes more.
5. Divide rice among plates or bowls. Spoon the stir-fry over the rice. Sprinkle sesame seeds on top.