Whisk together the soy sauce, honey, lemon juice, sesame oil, and cornstarch in a small bowl 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 them to a small bowl and set aside.
Increase heat to medium, add the olive oil to the same skillet, then add the cubed chicken and cook until lightly golden and cooked through, about 5–8 minutes.
Add the chopped onion, finely chopped ginger, broccoli florets, and black pepper to the skillet; sauté together for about 4 minutes until the vegetables are tender-crisp.
Reduce heat to medium-low, pour in the reserved soy-cornstarch mixture, 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, give it a final toss, and serve immediately.
