Steamed Chicken with Mushrooms and Chinese Sausage

Name: Steamed Chicken with Mushrooms and Chinese Sausage
Ingredients: 1 1/2 ounces (about 2 cups) dried sliced shiitake mushrooms; 1 1/2 pounds skinless, boneless chicken breasts, thinly sliced; 2 tablespoons oyster sauce; 4 teaspoons cornstarch; 1 teaspoon toasted sesame oil; 1/2 teaspoon freshly grated ginger; 1/4 teaspoon sugar; Kosher salt and freshly ground white pepper; 3 links Chinese sausage, thinly sliced on the bias; 2 scallions, thinly sliced; 12 ounces (about 5 cups) broccoli florets, cut into similar sizes; Steamed white rice, for serving