Pour the chicken broth into a bowl and add the reduced-sodium soy sauce, light brown sugar, sesame oil, and cornstarch.
Peel and finely grate 1 teaspoon fresh ginger. Prepare 1 teaspoon minced garlic, equivalent to approximately 2 small cloves, and add both to the bowl along with ¼ teaspoon black pepper.
Whisk the mixture thoroughly until evenly blended, then place the sauce aside.
Separate 1 pound of broccoli into florets, yielding approximately 5 cups.
Cut the white button mushrooms into thick slices and slice the yellow onion into strips.
Cut the boneless, skinless chicken breast into bite-sized pieces measuring approximately ¾ inch in thickness.
Lightly season the chicken pieces with black pepper.
Place a large skillet or wok over medium-high heat and add 1 tablespoon of the oil.
When the pan is thoroughly heated, arrange the chicken in a single layer. Allow it to sear without stirring for 1 minute.
Stir the chicken and continue stir-frying for approximately 5 minutes, or until the pieces are completely cooked and develop a golden exterior.
Remove the chicken from the skillet and transfer it to a plate.
Pour the remaining 1 tablespoon oil into the same skillet.
Add the onion, mushrooms, and broccoli to the hot pan.
Cook for approximately 3 minutes while stirring continuously, until the vegetables become tender while retaining a pleasant texture.
Lower the heat to medium-low.
Give the prepared sauce another thorough stir to redistribute the ingredients, then pour it over the vegetables in the skillet.
Allow the mixture to simmer for 3–4 minutes, stirring regularly, until the sauce thickens and the ingredients are well combined.
For a thinner consistency, incorporate water 1 tablespoon at a time until the sauce reaches the preferred texture, then return the mixture to a simmer.
Add the cooked chicken back to the skillet and stir for approximately 30 seconds, or until heated through.
Taste the stir-fry and add additional soy sauce if further seasoning is desired.
Serve the chicken and broccoli stir-fry over fluffy white rice and finish with toasted sesame seeds.