Make the Sauce - In a small bowl, combine all of the sauce ingredients and whisk to dissolve sugar and corn starch. Set sauce aside.
Prepare Chicken - Cut chicken into small bite-sized pieces and season lightly with 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.
Stir Fry Veggies - In the same skillet, add another 1 Tbsp oil along with broccoli florets, sliced onion and sliced mushrooms. Stir fry 3 minutes or until mushrooms are softened and broccoli is crisp-tender then reduce heat to medium/low.
Add Sauce - 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 water a tablespoon at a time.
Combine and Serve - 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.
