1. In a large, heavy saucepan, combine the tomatoes, carrot, onion, celery, a pinch of salt, and basil. Cover the pot and cook over medium heat until the mixture comes to a simmer. Uncover and cook, stirring occasionally, 20 minutes or until the sauce is thickened.

2. Let cool slightly. Pass the sauce through a food mill or puree it in a food processor or blender. Reheat gently and taste for seasoning. Stir in the oil. Serve hot. Can be made ahead and stored in a tightly sealed container in the refrigerator up to 5 days or in the freezer up to 2 months.