Whisk together soy sauce, honey, lemon juice, sesame oil, and cornstarch. Set mixture aside.
Over medium-low heat in a large skillet or wok, toast sesame seeds for 2 minutes, or until fragrant. Place toasted seeds in a bowl and set aside.
Add olive oil to the same skillet, turn to medium heat and cook chicken until lightly golden. Add onions, ginger, broccoli, and pepper. Sauté for 4 minutes.
Reduce heat to medium-low, add soy sauce mixture and toss to combine. Cook until sauce is desired thickness, but no more than 5 minutes.
Sprinkle with toasted sesame seeds and serve. Enjoy Chicken and Broccoli Stir-Fry with brown rice or quinoa.