
In a small bowl, whisk broth, soy sauce, garlic, honey, cornstarch, ginger, and sesame oil until cornstarch is dissolved.
In a large skillet or wok over high heat, heat neutral oil. Cook chicken, undisturbed, until it easily releases from pan, 1 to 2 minutes. Stir and continue to cook, stirring occasionally, until golden brown on all sides and just cooked through, about 5 minutes more. Transfer to a plate.
In same skillet over medium-low heat, toss broccoli in broth mixture. Cover skillet and let broccoli steam until crisp-tender, 2 to 3 minutes.
Uncover and return chicken and any accumulated juices to skillet. Cook, stirring, until sauce is thickened and chicken and broccoli are well coated, 1 to 2 minutes more.
Divide rice among plates or bowls. Spoon stir-fry over. Top with sesame seeds.