In 10- or 12-inch skillet over medium-high heat, in hot salad oil, cook steaks, a few at a time, 2 or 3 minutes on each side or until of desired doneness; place on warm platter and keep warm. Chop 3 tomatoes and slice the rest.
Reduce heat to medium: to same skillet, add 1/4 cup water, chopped tomatoes, green onions, sugar, salt and basil. Blend cornstarch and 1/4 cup water until smooth; gradually stir into tomato mixture and cook, stirring, until thickened. Add sliced tomatoes; cook until heated through. Spoon tomato mixture over steaks.