In 2-quart saucepan, mix rice mixture ingredients. Heat to boiling. Reduce heat to low; cook uncovered 20 to 25 minutes, stirring occasionally, until creamy. Remove from heat; cool 10 minutes.
Heat oven to 350°F. Lightly grease 8-inch square (2-quart) glass baking dish with shortening or cooking spray. In large bowl, beat eggs with wire whisk until blended. Stir in remaining pudding ingredients and the rice mixture. Pour into baking dish.
Bake 55 to 60 minutes or until set. Serve warm or cold. If desired, serve with whipped cream. Store in refrigerator.