Chinese Stir Fried Tomatoes and Eggs

Name: Chinese Stir Fried Tomatoes and Eggs
Ingredients: Steamed rice, for serving (I suggest 4 cups uncooked rice, cooked according to package directions); Ginger Scallion Sauce, for serving (recipe follows); 12 eggs; Salt, to taste; 1 teaspoon sesame oil; 2 tablespoon Shaoxing rice wine or dry sherry; 2 teaspoons cornstarch; 2 teaspoons sugar; 4 tablespoons ketchup; 2 pounds beefsteak tomatoes in-season, or canned diced tomatoes in juice (one 32-ounce can); 8 tablespoons vegetable oil; 6 scallions, sliced; 2 teaspoons minced ginger (about 1⁄2-inch piece); 2 ounces ginger (about a 3-inch piece), peeled and cut into 1⁄2-inch chunks; 6 ounces scallions (1 large or 2 small bunches), cut into 1-inch lengths; 2 teaspoons sea salt, plus more to taste; 1 cup peanut or vegetable oil