Prepare the Sauce: Whisk together all the sauce ingredients in a bowl. The warm broth will help dissolve the sugar faster. Set aside.
Cook the Chicken: Season the chicken lightly with pepper and fry it in a heated skillet with some oil. Once golden brown and cooked through, remove and keep warm.
Cook the Vegetables: In the same skillet, stir fry the broccoli, onion, and mushrooms with some oil until softened.
Add the Sauce: Pour the sauce over the vegetables, simmer until thickened. If needed, add a bit of water to thin the sauce.
Combine and Serve: Add the chicken back into the pan, stir until heated through. Taste and add more soy sauce if needed. Serve this delightful dish over hot rice.