Heat the vegetable oil in a large pot over medium-high heat. Add the scallion whites and cook until slightly tender, 2 to 3 minutes. Stir in the ginger and cook about 1 minute. Add 7 cups water, the soy sauce, sugar, salt to taste, 3/4 teaspoon pepper and the mushrooms. Cover and bring the broth to a simmer. Mix the cornstarch with 1/4 cup cold water and gradually stir into the broth. Bring to a gentle boil, stirring; the broth will thicken slightly. Add the scallion greens, tomatoes and white fish to the broth, and simmer until the fish is opaque, about 3 minutes. Add the scallops, vinegar, and salt and pepper to taste (the scallops will cook instantly from the heat of the soup). Ladle into bowls.