In a small bowl, whisk together the cornstarch, sugar, soy sauce, and toasted sesame oil.
Place the chicken strips in a plastic bag or bowl, pour the marinade over the chicken, toss to coat, and refrigerate for at least 15 minutes or up to 12 hours.
Heat 1 tablespoon of oil in a wok or large sauté pan over medium-high heat. When hot, add the marinated chicken and cook until cooked through, about 4–6 minutes depending on thickness. Transfer the chicken to a plate and tent with foil.
Return the pan to the heat and add a couple tablespoons of the reserved water to deglaze the pan, scraping up browned bits.
Add the chopped onion and minced garlic to the pan and cook about 3 minutes, until the onion begins to turn translucent at the edges.
Add the green beans and diced red bell pepper and cook about 3 minutes; then add 2 tablespoons of the reserved water and cover. Cook, adding more water as needed, until the vegetables reach your desired doneness, about 3–8 more minutes.
Return the cooked chicken to the pan, stir to combine, and heat through. Season with salt to taste.
Serve the string bean chicken over white steamed rice.