In a medium bowl combine eggs and basil; set aside. Heat oil in a large broilerproof skillet; add corn, zucchini, and green onions. Cook and stir for 3 minutes; add tomatoes. Cook, uncovered, over medium heat about 5 minutes or until vegetables are crisp-tender, stirring occasionally.
Pour egg mixture over vegetables in skillet. Cook over medium heat. As mixture sets, run a spatula around edge of skillet, lifting egg mixture so uncooked portion flows underneath. Continue cooking and lifting edges until egg mixture is almost set (surface will be moist). Sprinkle with cheese.
Place the skillet under broiler 4 to 5 inches from heat. Broil 1 to 2 minutes or until top is just set and cheese is melted. Makes 4 servings.