Slice chicken breast across the grain into strips about 1/4 inch thick. In a bowl, toss the chicken with the cornstarch, sherry, salt, and pepper. Make sure it’s coated evenly. Set aside for 10 to 15 minutes.
Pour about an inch of water into the pot and put the steamer basket in. Cover and bring to a boil. Place broccoli florets in basket and steam just until the color starts to shine, about 3 minutes. Turn off the heat.
In a wok, heat oil over high heat for about a minute. Add garlic and ginger and stir-fry for just 30 seconds. Add the chicken and stir-fry until it is white and opaque, about 3 to 5 minutes. Add the broccoli, soy sauce, oyster sauce, chicken broth, and sugar. Stir-fry until broccoli is tender and heated through, about 2 to 3 minutes.