Heat the oil or water in a large pot over medium heat. Add the onion, carrots, and garlic and cook, stirring frequently, until the vegetables begin to soften, about 5 minutes. Add the rice, tomatoes, broth, bay leaf, and the dried basil, oregano, and thyme (if using), and bring to a boil. Reduce the heat to a simmer, cover, and cook for 15 minutes.