Add the chicken pieces, soy sauce, 2 tablespoons chicken broth, and cornstarch to a large bowl. Toss until the chicken is evenly coated.
Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat.
Add the zucchini, green bell pepper, broccoli, and garlic. Cook while stirring frequently for 2–3 minutes.
Pour in 1/2 cup chicken broth. Cover and simmer for 4–5 minutes, or until the vegetables are tender but still slightly crisp.
Transfer the vegetables and cooking liquid to a bowl. Carefully wipe the skillet clean.
Heat the remaining tablespoon of vegetable oil over medium-high heat. Add the marinated chicken and stir-fry for about 5 minutes, until cooked through and no longer pink in the center. For food safety, chicken should reach an internal temperature of 165°F (74°C).
Return the vegetables and their cooking liquid to the skillet. Toss everything together and cook for another 2–3 minutes, allowing the sauce to lightly coat the chicken and vegetables.
Sprinkle the green onions over your Chicken and Vegetable Stir Fry and serve warm.