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In frying pan, heat oil on medium heat. In a bowl, crack eggs and stir eggs until thoroughly mixed.
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Add vegetables to pan and sauté until soft. Add eggs to vegetables and cook for 2 minutes. Add shredded cheese to the top of eggs and cover pan with a lid. Cook for 5 minutes or until cheese is melted and eggs are firm.
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Remove from pan and cut into four servings. Sprinkle with chopped basil leaves.