In a medium bowl, toss the sliced chicken with 1 tablespoon soy sauce and 1 tablespoon cornstarch. Let sit for 10 minutes to velvet.
In a small jar or bowl, whisk together chicken broth, 3 tablespoons soy sauce, oyster sauce, brown sugar, sesame oil, ginger, garlic, and 1 teaspoon cornstarch. Set aside.
Heat 1 tablespoon oil in a large wok or skillet over medium-high heat. Add chicken in a single layer. Cook for 3-4 minutes per side until golden and cooked through. Remove chicken from pan and set aside.
Add the remaining 1 tablespoon oil to the hot pan. Add broccoli and sliced carrots. Stir fry for 2 minutes.
Add 2 tablespoons of water to the pan and cover immediately to steam the veggies for 2-3 minutes until tender-crisp.
Remove the lid and let any remaining water evaporate. Add the cooked chicken back to the pan.
Whisk the sauce mixture once more and pour over the chicken and vegetables. Toss everything together for 1-2 minutes until the sauce thickens and coats the ingredients glossy.
Serve immediately over steamed white rice or noodles.