Make the tomato flavoring: in a blender or food processor, combine the tomatoes with the onion and garlic and blend to a smooth puree.
Fry the raw rice: in a medium (3-quart) saucepan with a tight-fitting lid, heat the oil over medium. Add the rice and stir frequently until the kernels turn from translucent to milky white, 5 to 6 minutes (some browning is fine). Add the tomato puree, stir, and cook until reduced and somewhat dry-looking, 2 to 3 minutes.
Simmer the rice: add the broth or water and bring to a full boil. Add the chiles, parsley, and salt (about 3/4 teaspoon with lightly salted broth, 1 1/2 teaspoons with unsalted broth or water). Stir, scraping down the sides. Cover and cook over lowest heat 20 minutes, until the rice is tender.
Fluff gently with a fork to release the steam, re-cover, and let stand a few minutes. Remove the chiles if you like, or pull them out to decorate the top.