Bring the water to a boil and add the rice. Add salt to taste, bring back to a boil, reduce heat, cover, and simmer for about 40 minutes, until the rice is tender. Drain and toss with the broccoli, nuts, and parsley. [Meanwhile, steam broccoli and chop nuts.] Mix together the lemon juice, vinegar, garlic, and yogurt. Whisk in the walnut oil and add salt and pepper. Toss with the rice mixture, correct the seasonings, and serve; or refrigerate until shortly before serving. Note: If the salad is to be refrigerated for a long time, add the broccoli and parsley shortly before serving to retain their bright color. [Shulman says this serves 4-6. We think 3-4.]