In a small saucepan add the pomegranate juice. Bring to a boil and then simmer for about 5 minutes or until reduced to about 2 tablespoons. Remove from heat.
Put the walnuts and bread crumbs into a food processor and process until finely ground. Add the reduced pomegranate juice, lemon juice, roasted red peppers, cayenne pepper and cumin and process until smooth. With the processor on add the olive oil in a thin stream. Season with salt, to taste. Serve.