Gingery Seafood Soup

Name: Gingery Seafood Soup
Ingredients: 1 tablespoon vegetable oil; 1 bunch scallions; whites cut into 1/4-inch pieces,greens cut into 2-inch pieces; 1 tablespoon minced peeled ginger; 1 tablespoon low-sodium soy sauce; 1/2 teaspoon sugar; Kosher salt and freshly ground pepper; 4 ounces shiitake mushrooms, stemmed and sliced; 1/4 cup cornstarch; 2 plum tomatoes, cored and cut into large chunks; 12 ounces firm white fish (such as pollock), cut into 1-inch pieces; 6 ounces bay scallops; 2 tablespoons balsamic vinegar