In a bowl, add the chicken pieces, soy sauce, sesame oil, and cornstarch. Mix well until the chicken is fully coated. Set aside for a few minutes.
Heat a pan or wok over medium-high heat. Add cooking oil.
Add the chicken to the pan and cook for about 5–7 minutes until it turns golden brown and fully cooked. Remove the chicken and keep aside.
In the same pan, add a little more oil if needed. Add minced garlic and grated ginger. Stir for about 30 seconds until fragrant.
Add bell peppers and broccoli florets. Stir-fry for 3–4 minutes until slightly soft but still crunchy.
In a small bowl, mix honey, brown sugar, rice vinegar, and a little soy sauce.
Pour this sauce into the pan with the vegetables. Stir well.
Add the cooked chicken back into the pan. Mix everything together so the chicken is coated with the sauce.
Cook for another 2–3 minutes until the sauce thickens slightly.
Turn off the heat. Sprinkle sesame seeds and chopped green onions on top.
Serve hot and enjoy your homemade sesame chicken stir fry!