Heating the liquid. In a small saucepan or microwave oven, heat the broth or water until steaming; stir in about ¾ teaspoon salt if using salted broth, 1 ½ teaspoons if using unsalted broth or water. Cover and keep warm.
Frying the rice. In a medium (3-quart) saucepan (one that’s about 8 inches in diameter is perfect for even cooking) with a tight-fitting lid, heat the oil over medium. When hot, add the raw rice and onion, and stir regularly until the grains have turned from translucent to milky-white, 4 to 5 minutes. Add the garlic and stir for a few seconds, until fragrant. For beautiful white rice, the grains should not brown.
Simmering the rice. Add the warm liquid and lime juice, stir thoroughly and scrape down any grains that are clinging to the side of the pan. Cover and cook over lowest heat for 15 minutes—the temperature should be low enough that only the slightest hint of steam escapes from the lid.
Remove the pan from the heat and let stand covered for 5 minutes. Uncover and test a grain of rice: If it’s still a little hard, re-cover and set over low heat for about 5 minutes; if the rice has absorbed all the liquid (and is completely dry), sprinkle on 2 tablespoons of water before returning it to the heat.
As soon as the rice is done, sprinkle on the parsley and gently fluff the rice to release the steam and stop the cooking, then turn it into a warm bowl. It’s ready to serve.
Working Ahead: The rice can be successfully made ahead, turned out onto baking sheet to cool in a shallow layer, covered and refrigerated up to 3 days. When ready to serve, reheat in a microwave oven or a steamer. Or reheat on a baking sheet (covered with foil) in a 325 degree oven until heated through, about 15 minutes, before tossing in the parsley and serving.