In a large pan on medium-high heat, add 1 tablespoon of oil. Once the oil is hot, add chicken, season with salt and pepper, and sauté until cooked through and lightly browned. Remove cooked chicken and set aside.
In the same pan, heat 1 tablespoon of oil and add mushrooms. Cook till soft and then add broccoli florets. Continue to cook until broccoli is tender, approximately 4 minutes. Remove veggies from pan and set aside.
Add final tablespoon of oil to the pan and garlic and ginger. Cook until fragrant. Add the remaining ingredients for the sauce into the pan and stir until smooth (with a whisk is best).
Return chicken and vegetables back to the pan, and cook until heated through.
Serve over rice or noodles.