In a small bowl, whisk together the soy sauce, teriyaki sauce, honey, rice vinegar, and cornstarch until well combined. Set aside.
Heat the cooking oil in a large skillet or wok over medium-high heat. Add the minced garlic and grated ginger and cook for 1-2 minutes until fragrant.
Add the chicken strips to the skillet and stir-fry for 5-6 minutes until cooked through and browned.
Add the broccoli florets, bell pepper, carrot, and snap peas to the skillet. Stir-fry for an additional 3-4 minutes until the vegetables are crisp-tender.
Pour the prepared teriyaki sauce over the chicken and vegetables. Stir well to coat everything evenly. Cook for another 1-2 minutes until the sauce thickens.
Remove the skillet from heat and garnish with sliced green onions and sesame seeds.
Serve the stir fry teriyaki chicken over steamed rice or noodles.