Whisk together first 4 ingredients and 1/4 cup Parmesan in a large bowl; set aside.
Heat 1 tablespoon oil over low heat in a 10-inch heavy, ovenproof skillet. Add garlic, and cook 1 minute or until golden; transfer to a large bowl with a slotted spoon. Add 3 tablespoons oil to skillet, increase heat to medium-high, and cook potatoes, stirring occasionally, 7 minutes or until tender. Transfer to bowl with garlic. Add corn; cook 1 minute or until heated through. Transfer to bowl with garlic and potatoes.
Add 1 tablespoon oil to skillet. Stir in tomatoes, and cook, stirring frequently, 3 to 5 minutes or until they begin to brown and the skins split. Add reserved potato mixture to skillet, and spread evenly over bottom.
Preheat broiler. Pour egg mixture over vegetables. Cook about 4 minutes, lifting up eggs around the edges. Reduce heat to medium, cover, and cook about 5 more minutes. (The center will still be moist.)
Remove lid, and broil 4 minutes or until eggs are set; sprinkle top with remaining cheese, and broil 2 to 3 minutes or until golden brown. Loosen edges with a spatula before cutting into serving pieces.