Mix chicken, soy sauce, sherry, and cornstarch in a bowl.
Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat; cook and stir broccoli, bell pepper, zucchini, and garlic for 2 to 3 minutes. Add chicken broth, cover, and simmer until vegetables are tender, 4 to 5 minutes. Transfer vegetables and sauce to a large bowl and wipe skillet clean.
Heat remaining 1 tablespoon vegetable oil over medium-high heat; cook and stir chicken until meat is no longer pink in the center, about 5 minutes. Stir in vegetables; continue to cook and stir for 2 to 3 minutes more. Sprinkle with green onions.