In a small saucepan, whisk together soy sauce, water, mirin, brown sugar, honey, ginger, and garlic.
Bring the sauce to a simmer over medium heat for 5 minutes, then stir in the cornstarch slurry and cook until thickened. Set aside.
Heat vegetable oil in a large wok or heavy-bottomed skillet over high heat until shimmering.
Add the chicken pieces to the wok in a single layer and sear until browned and cooked through, approximately 5-7 minutes. Remove chicken and set aside.
Add broccoli, bell pepper, and carrot to the same wok and stir-fry for 3-4 minutes until vegetables are crisp-tender.
Return the cooked chicken to the wok and pour the prepared teriyaki sauce over the ingredients.
Toss the mixture continuously for 1-2 minutes until everything is evenly coated and the sauce is bubbling.
Remove from heat and garnish with toasted sesame seeds and sliced green onions before serving.