In a food processor, place all the ingredients for the walnut and olive mixture and pulse until you have a grainy paste. Adjust seasoning to taste. Cover and refrigerate for 15 minutes and up to 3 days.
Just before serving, garnish with walnuts, fresh pomegranate arils, whole olives, and cilantro. Serve as a dip with toasted bread cut into 4-in/10cm pieces, or