Combine all of the sauce ingredients in a small bowl. Whisk to dissolve sugar and cornstarch (warm broth will help dissolve the sugar faster). Set aside.
Season cut chicken lightly with salt and pepper. Heat a large heavy skillet or wok over medium-high heat. Add 1 tbsp oil. Add chicken in a single layer and let it sit undisturbed for 1 minute to get a good sear then stir fry for another 5 minutes or until golden brown just cooked through then remove to a bowl and loosely cover to keep warm.
In the same skillet, add another 1 tbsp oil along with broccoli florets, onion and mushrooms. Cook for 3 minutes or until mushrooms are softened and broccoli is crisp-tender then reduce heat to medium/low.
Give the sauce a quick stir and pour all of it over the vegetables. Simmer 3-4 minutes or until sauce is thickened and garlic and ginger are mellowed in flavor. To thin the sauce, add broth a tablespoon at a time.
Return chicken to the pan and stir another 30 seconds or until heated through. Add more soy sauce to taste if needed and serve over hot rice.