Toss sliced chicken with cornstarch, salt, and black pepper; set aside
Whisk chicken broth, soy sauce, oyster sauce, hoisin sauce, brown sugar, sesame oil, and cornstarch until smooth
Heat 1 tablespoon oil in a large skillet or wok over medium-high heat
Add chicken in a single layer and cook until lightly browned and just cooked through
Remove chicken from pan and set aside
Add remaining oil to the pan
Stir in garlic and ginger and cook 20–30 seconds until fragrant
Add broccoli, carrots, bell pepper, and snow peas and stir-fry 3–4 minutes until crisp-tender
Return chicken to the pan
Pour in sauce and stir constantly until thickened and glossy, about 1–2 minutes
Stir in green onions and remove from heat