In a wok or frying pan, boil about six cups of water with a generous amount of salt and ground pepper.
With the water boiling briskly, drop in the chicken pieces. Stir once to separate. Cook just until the chicken meat changes color. Scoop out and transfer to a plate.
Bring the water to a hard boil once more. Drop in the broccoli florets and cook for one minute. Scoop out and transfer to another plate.
Make the sauce by stirring together the broth, starch and sugar.
Clean out the wok or frying pan. Pour in the sesame seed oil and heat. Saute the garlic and ginger with a bit of salt and pepper until fragrant and lightly browned.
Turn up the heat. Add the chicken and broccoli to the pan. Sprinkle with salt and pepper. Stir fry for a minute.
Pour in the sauce. Cook, stirring, until thick and clear. Taste and add more salt and pepper, as needed.
Serve the chicken broccoli stir fry immediately. You may want to garnish it with toasted sesame seeds.