In a saucepan, heat the oil until shimmering. Add the onion and garlic and cook over moderate heat, stirring, until softened and just starting to brown, 10 minutes. Add the carrot and thyme and cook, stirring, until softened, 5 minutes. Add the tomatoes and their juices and bring to a boil. Simmer over moderately low heat, stirring, until thickened and reduced to 5 cups, 30 minutes. Season with salt.