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Bring 2 cups (500 mL) salted water to boil in medium saucepan, Add vegetables and cover. Cook just until tender, then drain. Cut any larger vegetables.
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Whisk eggs, basil, salt and pepper in small bowl.
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Heat oil in 10-inch (25 cm) non-stick skillet over medium heat. Add onion and garlic; cook, stirring occasionally, until soft, about 4 minutes.
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Stir in cooked vegetables. Pour egg mixture over vegetables in skillet. As mixture sets around edge of skillet, with spatula, gently lift cooked portions to allow uncooked egg to flow underneath. Cover and cook until bottom is set and top is almost set.
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Sprinkle cheese over top. Cover skillet with lid and cook for another minute to melt cheese.
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Cut frittata into wedges to serve.