In a large bowl, combine the rice with enough very hot tap water to cover. Stir and let sit for about 10 minutes. Drain, rinse in cold water, and drain again, shaking thoroughly. In a blender, combine the tomatoes, onion, and garlic and blend until smooth, scraping down the sides of the container as necessary. Set aside.

In a large heavy saucepan, heat the oil over mediumhigh heat. Add the rice and cook, stirring occasionally, until the rice turns a light golden color, about 10 minutes. Do not let it scorch. Add the tomato puree and fry, scraping the bottom of the pan to stop the mixture from sticking, for 6 to 8 minutes, or until all the liquid has been absorbed. Add the chicken broth, carrots, zucchini, and giblets, if using. Stir in the salt and reduce the heat to mediumlow. Cook the rice uncovered and undisturbed until almost all of the broth has evaporated and little air holes form in the surface. Cover the top of the pan with a towel and the lid, reduce the heat to very low, and cook for 5 minutes more. Remove the pan from the heat and let rest for 10 minutes more, so that the rice can absorb the steam and swell. Just before serving, turn the rice over from the bottom so that the juices are redistributed.