Heat broth small saucepan over moderate heat until hot, then sprinkle saffron, salt and pepper into liquid and stir. Remove from heat. Set aside. (You will notice the broth has started to take on the lovely amber color from the saffron).
In a separate 2-quart heavy saucepan cook onion and butter over medium heat, stirring occasionally, until golden brown, approximately 5 minutes.
Add rice into onions and cook, stirring, until pale golden, about 3 minutes. Stir in saffron broth, and bring to a boil.
Reduce heat to low and cook, covered, until rice is tender and liquid is absorbed, about 20 minutes. Remove from heat and let stand, covered, 5 minutes, then fluff rice with a fork and fold in walnuts. Garnish with basil and serve.