In a 12 to 14-inch saute pan, heat the olive oil over medium-high heat and add the garlic. Cook over high heat until golden, about 2 minutes, then add the olives, and cook for 3 minutes, until softened.
Add the tomato sauce, then lower the heat, and simmer for 15 to 20 minutes, occasionally basting with the tomato sauce.
In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion and garlic, and cook until soft and light golden brown, about 8 to 10 minutes. Add the thyme and carrot, and cook 5 minutes more, until the carrot is quite soft. Add the tomatoes and juice and bring to a boil, stirring often. Lower the heat and simmer for 30 minutes until as thick as hot cereal. Season with salt and serve. This sauce holds 1 week in the refrigerator or up to 6 months in the freezer.
Yield: 4 cups