Cook the udon noodles according to package instructions. Drain and set aside.
In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the chicken pieces and cook until browned and cooked through, about 5-7 minutes.
Add the broccoli, bell peppers, and carrots to the skillet. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Stir in the minced garlic and cook for an additional 30 seconds until fragrant.
In a small bowl, whisk together the soy sauce, honey, rice vinegar, and cornstarch mixture. Pour this sauce over the chicken and vegetables in the skillet.
Cook for another 2-3 minutes, stirring constantly, until the sauce thickens and coats the chicken and vegetables.
Add the cooked udon noodles to the skillet and toss everything together until well combined. Drizzle with sesame oil and mix again.
Serve hot, garnished with sliced green onions and sesame seeds.