In a large nonstick saucepan, heat the olive oil and butter over moderately high heat. Add onions and garlic. Lower the heat to moderately low and cook for 25 minutes or until the onions are very soft and goden, stirring often.
Stir in tomatoes, broth, tomato sauce, thyme, bay leaf, sugar, salt, and pepper. Bring to a boil. Lower the heat and sinner, covered, for 15 minutes. Discard the bay leaf. Stir in the minced parsley.