Prep the Chicken: Slice the chicken against the grain into thin, bite-sized pieces (no thicker than 1/4 inch).
Place the chicken in a bowl, add marinade ingredients, and mix well. Let sit for 10 minutes.
Make the Sauce: Combine all sauce ingredients in a measuring cup or medium bowl and stir well. Keep aside.
Steam the Broccoli: In a large skillet, bring 1/3 cup of water to a boil over medium-high heat.
Add broccoli, cover, and steam for 1-2 minutes until tender. Transfer to a plate and wipe the skillet dry.
Cook the Chicken: Heat oil in the skillet, spread chicken in a single layer, and cook for 30 seconds without touching until browned.
Flip the chicken pieces to cook the other side for a few seconds, then stir and cook until the surface is lightly charred and the inside is still pink.
Combine Ingredients: Add the garlic and ginger to the skillet and stir a few times to release their fragrance.
Return broccoli to the skillet.
Stir the sauce again, pour into the skillet, and cook until it thickens (about 1 minute).
Serve: Transfer the stir-fry to a plate and serve hot with steamed rice or boiled noodles as a main dish.