Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium heat. Add the marinated chicken and cook for 3-4 minutes until nearly cooked through and lightly browned. Remove the chicken from the pan and set aside.
4. Stir-Fry the Vegetables:
Add the remaining tablespoon of oil to the pan. Sauté chopped garlic and ginger for 30 seconds until fragrant. Add broccoli florets and carrots, and stir-fry until the vegetables are tender, about 4-5 minutes.
5. Combine and Cook:
Return the cooked chicken to the pan. Pour the prepared sauce over the chicken and vegetables. Stir to combine and cook for an additional 2-3 minutes, allowing the sauce to thicken slightly and coat the ingredients evenly.
6. Garnish and Serve:
Garnish with sesame seeds and chopped green onions if desired. Serve hot over steamed or fried rice.
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