Place the soy sauce, water, garlic, ginger, honey, brown sugar and sesame oil in a small pot over medium-high heat. Cook for 2 minutes. Turn up the heat to high and bring to a boil.
Mix the cornstarch with 2 tablespoons of cold water until dissolved. Add the cornstarch mixture to the sauce and boil for 1-2 minutes or until sauce has thickened. Set sauce aside.
For the stir fry:
Heat 1 teaspoon vegetable oil in a large pan over medium-high heat. Add the broccoli and red peppers and season with salt and pepper. Cook for 4-5 minutes or until the vegetables have started to brown and soften. Add 2 tablespoons of water and cook, until water has evaporated. When your vegetables are crisp & tender, remove them from the pan and set aside; cover to keep warm.
Wipe out the pan. Heat the remaining 2 teaspoons of oil in the pan over high heat.
Place half of the chicken in the pan and season generously with salt and pepper. Cook for 3-4 minutes on each side or until cooked through. Set the first batch of chicken aside and repeat the process with the rest of the chicken.
Add all of the chicken and vegetables back to the pan. Pour the sauce over the top and cook for 2-3 minutes over medium-high heat until warmed through.