In a saucepan cook the onion in the oil over moderately low heat, stirring, until it is softened, add the rice, and cook the mixture over moderate heat, stirring, for 1 minute. Stir in the salt, the water, and the broth, bring the liquid to a boil, and cook the mixture, covered, over low heat for 18 to 20 minutes, or until the liquid is absorbed. Add the apricots, fluff the rice with a fork, and let the mixture stand, covered, off the heat for 5 minutes. Stir in the pine nuts, the parsley, and pepper to taste. Serve the pilaf with pot roast, lamb, or poultry.