In a large saucepan, combine the rice, soy milk, and salt and bring to a boil over high heat. Reduce heat to medium and simmer, stirring frequently, until the rice is soft, about 30 minutes.
Stir in the sugar and continue to cook for 5 minutes or until the sugar is dissolved and the pudding has thickened. Remove from heat, stir in the walnuts and the vanilla, and set aside to cool.
When the pudding is cooled, stir in the chocolate chips. Spoon the pudding into dessert bowls, then cover and refrigerate for at least 1 hour before serving.
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