In a medium bowl, combine the bite-sized chicken pieces with the soy sauce and cornstarch. Mix well until every piece of chicken is evenly coated.
Heat the cooking oil in a large skillet or wok over medium-high heat.
Add the coated chicken to the hot pan in a single layer. Cook for 4–5 minutes, stirring occasionally, until the chicken is lightly browned on all sides.
Add the minced garlic and grated fresh ginger. Stir constantly for about 30 seconds until fragrant.
Add the sliced red bell pepper and broccoli florets. Stir-fry for 3–4 minutes until the vegetables are tender-crisp.
In a small bowl, mix together the honey, brown sugar, rice vinegar, and sesame oil until well combined.
Pour the sauce into the pan. Stir well so the chicken and vegetables are evenly coated.
Cook for another 2–3 minutes, stirring frequently, until the sauce thickens slightly and becomes glossy.
Sprinkle the sesame seeds over the stir fry and mix everything together.