Whisk soy sauce, honey, vinegar, sesame oil, and cornstarch mixture in small bowl; set aside.
Heat 2 tablespoons vegetable oil in large wok or skillet over high until smoking hot.
Stir-fry pepper, broccoli, peas, and carrots 4-5 minutes until crisp-tender; remove to plate.
Add remaining 1 tablespoon oil; cook garlic and ginger 30 seconds until fragrant.
Stir-fry chicken 2 minutes until heated through with slightly crispy edges.
Return vegetables; add sauce and toss 1-2 minutes until thickened and coating evenly.
Garnish with green onions and sesame seeds; serve immediately over rice.