Add the garlic, ginger, green onion whites, and carrots. Stir fry for 30 to 40 seconds until fragrant. Turn the heat back to high.
Add broccoli & other veggies and a splash of cooking wine (1 teaspoon), then stir fry for 1.5 to 2 minutes.
Add back in chicken and stir fry for 30 seconds.
Give the sauce a stir and pour into the center of the wok. Stir fry to mix for 15 to 20 seconds. Taste and adjust seasoning if needed. My dad thought it could use more sugar (0.50 teaspoon).
Add in cornstarch slurry a bit at a time, while stirring, around 30 seconds. Check the thickness. There's no need to use all if you reach the desired consistency.
Add a splash of sesame oil (1/2 teaspoon), stir to mix, then turn the heat off.