Preheat broiler to the high setting.
In a large skillet, heat the olive oil over medium-high heat. Add the onions and saut� until tender. Add the tomatoes and cook for an additional five minutes.
Cool the tomato mixture in a large bowl for 10 minutes. Then add salt, pepper, parmesan cheese, and basil, and stir.
Whisk the eggs and add them to the tomato mixture.
Heat the melted butter into a large skillet and cook the egg and tomato mixture over low heat until it thickens, about 10 minutes. Then broil until it is light brown.
