Combine all the ingredients in a small bowl. Whisk to dissolve corn starch and sugar. Warm broth will speed up the process. Set sauce aside.
Slice the chicken into bite-sized pieces, no more than 3/4 inch thick. Season with salt and pepper. Over medium heat, heat a large skillet or wok. 1 tablespoon oil. Allow the chicken to rest in a single layer. Stir fry for 5 minutes, or until it is golden brown.
Add 1 Tbsp oil to the skillet. Next, add broccoli florets and sliced onions. Finally, add sliced mushrooms. Stir fry for 3 minutes, or until the mushrooms are softened. When the broccoli is tender, turn down heat to medium/low.
Pour the sauce over the vegetables and give it a quick stir to prevent starch from settling. Let the sauce simmer for 3-4 minutes, or until it thickens and the garlic and ginger have mellowed in taste. Add a tablespoon of water to thin the sauce.
Stir the chicken for 30 seconds more or until it is cooked. Serve the chicken with hot rice and more soy sauce if necessary.