In a small bowl, whisk together the soy sauce (or tamari), honey, lemon juice, sesame oil, and cornstarch until smooth; set the sauce aside.
Heat a large skillet or wok over medium‑low heat and toast the sesame seeds for about 2 minutes, stirring, until fragrant; transfer the seeds to a small bowl and set aside.
Raise the heat to medium, add the olive oil to the same skillet, then add the cubed chicken and cook until lightly golden and mostly cooked through, about 5–7 minutes.
Add the chopped onion, finely chopped ginger, broccoli florets, and black pepper to the skillet; sauté for about 4 minutes until the vegetables are crisp‑tender.
Reduce the heat to medium‑low, pour in the reserved sauce, and toss everything to coat; cook, stirring, until the sauce thickens to your liking, up to 5 minutes.
Sprinkle the toasted sesame seeds over the stir‑fry and serve immediately.