Cut 2 pounds boneless skinless chicken breast into bite-sized cubes. Thinly slice 1/2 medium yellow onion and cut 1 medium red bell pepper and 1 medium green bell pepper into 1/2-inch strips. Prepare 2 cups broccoli florets, 2 cups snow peas, 1 cup shredded carrots, and 1/4 cup sliced green onion. Set all ingredients aside.
In a small mixing bowl, whisk together 1/2 cup water, 1/2 cup chicken broth, 2 tablespoons soy sauce, 2 tablespoons minced garlic, 1 tablespoon grated ginger, 2 teaspoons cornstarch and 1 teaspoon honey. Set aside.
Heat a large wok or skillet over high heat. Add 2 tablespoons vegetable oil and 2 tablespoons sesame oil.
Add the cubed chicken to the hot pan. Season with 1 teaspoon salt and 1 teaspoon black pepper. Cook, tossing occasionally, for 5 to 10 minutes, or until the chicken begins to brown and is mostly cooked through.
Add 2 tablespoons minced garlic and the prepared onion, bell peppers, broccoli, snow peas, and carrots. Cook for 5 minutes, stirring frequently, until the vegetables begin to soften.
Pour the sauce mixture into the pan. Stir and cook over medium heat for 5 minutes, or until the sauce thickens and everything is evenly coated.
Serve hot over rice or noodles. Garnish with sliced green onions.